Applied-Algebra WGU Applied Algebra FXO2 PFXP C957 Questions and Answers

From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.

That means the number of customers is:

" increasing slower and slower "

After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.

That means the number of customers is:

" decreasing faster and faster "

So the full description is:

" The number of customers increases slower and slower and then decreases faster and faster. "

Therefore, the correct answer is:

▭ ( " D " )

The regression function has:

r^2=0.54

This indicates a moderate fit, not a strong fit. The model explains some of the variation in the data, but not as strongly as a model with an r^2value closer to 1.

Now consider the prediction at:

x=20.6

From the scatterplot, the observed data values extend to about:

x=18

The prediction at x=20.6is beyond the observed data, so it is an extrapolation. However, it is not very far beyond the data range.

Because x=20.6is within a reasonable extrapolation range and the model has a moderate fit, the prediction is appropriate.

The graph shows a decreasing exponential function.

The horizontal axis represents:

" Time in months "

The vertical axis represents:

" New user accounts per day "

The graph starts near 7,000new user accounts per day and decreases over time. However, it does not decrease toward 0. Instead, the graph levels off near a horizontal value around:

y=2,500

This horizontal value is the horizontal asymptote.

A horizontal asymptote shows the long-term value the function approaches. Since the asymptote is above 0, the model predicts that the number of daily new user accounts approaches a positive value, not zero.

So the justified statement is:

" The number of daily new user accounts will not decrease to 0. "

The function is:

f(x)=330× 〖 1.15 〗 ^x

Because xrepresents the number of years since 2005:

2006 ⇒ x=1

2011 ⇒ x=6

The average yearly rate of change from 2006 to 2011 is:

(f(6)-f(1))/(6-1)

First, find f(1):

f(1)=330× 〖 1.15 〗 ^1

f(1)=330×1.15

f(1)=379.50

Now find f(6):

f(6)=330× 〖 1.15 〗 ^6

f(6)≈330×2.31306

f(6)≈763.31

Now calculate the average rate of change:

(763.31-379.50)/(6-1)

=383.81/5

=76.762

Rounded to two decimal places:

76.76

So the average yearly rate of change of the artifact’s value from 2006 to 2011 is approximately:

$76.76 " per year "

Therefore, the correct answer is:

▭ ( " A " )

This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139−39=100 dollars. Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.

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This question asks us to read and interpret a value from a graph.

The horizontal axis represents:

" Days since the beginning of the month "

The vertical axis represents:

" Practice duration in minutes "

We need to find the practice duration for:

" day " 9

To do this, locate 9on the horizontal axis, move upward to the blue graph, and then read the corresponding value on the vertical axis.

From the graph, the point at day 9is approximately:

127

So the musician practiced for:

127 " minutes "

The function is:

f(x)=10× 〖 1.09 〗 ^x

This is an exponential growth function because:

1.09 > 1

For an exponential growth function, the rate of increase becomes larger as time passes. That means later intervals usually have faster average increases than earlier intervals.

Since xrepresents years since 2001:

2001 ⇒ x=0

2003 ⇒ x=2

2005 ⇒ x=4

2013 ⇒ x=12

2016 ⇒ x=15

2019 ⇒ x=18

2021 ⇒ x=20

The latest interval is:

2013 " to " 2021

Because the graph is exponential growth and is steepest later in time, this interval has the fastest average increase.

The graph shows the temperature of an object changing over time.

The horizontal axis represents:

" Time in minutes "

The vertical axis represents:

" Temperature in degrees Fahrenheit "

The curve is decreasing quickly at first and then begins to level off. This is the shape of an exponential decay function.

A horizontal asymptote is a horizontal line that the graph approaches as time increases.

Because a horizontal asymptote is a horizontal line, its equation must have the form:

y= " constant "

From the graph, the temperature approaches about:

25^ ∘ F

So the horizontal asymptote is:

y=25

This means the object’s temperature gets closer and closer to 25^ ∘ Fover time.

From week 1 to week 7, the graph is increasing and becoming steeper.

In Applied Algebra, when a graph is increasing and its slope is getting larger, the quantity is said to be:

" increasing faster and faster "

This interval is on the early increasing part of the logistic curve, before the graph begins to level off.

Therefore, the correct answer is:

▭ ( " B " )

The graph shows the total value of an investment account as time increases.

The horizontal axis represents:

" Time in years "

The vertical axis represents:

" Total value in dollars "

We need to find the value of the account after:

8 " years "

From the graph, when t=8, the curve is slightly above $2,200. The closest answer choice is:

$2,221.12

So the value of the account after 8 years is approximately:

$2,221.12

Therefore, the correct answer is:

▭ ( " D " )

The graph models the number of widgets the manufacturing team can produce each day.

The horizontal axis represents:

" Days "

The vertical axis represents:

" Widgets produced each day "

The two labeled points are:

(16│9.1)

and

(18│12.4)

This means:

On day 16, the team could produce about 9.1widgets per day.

On day 18, the team could produce about 12.4widgets per day.

The average rate of change is:

(12.4-9.1)/(18-16)

=3.3/2

=1.65

Rounded to the nearest tenth:

1.7

So from day 16 to day 18, the team’s production increased by an average of about:

1.7 " widgets each day "

We are given the function:

d(x)=14+65x

This is a linear function because it has the form:

d(x)=mx+b

where 65is the rate of change and 14is the starting value.

We need to find:

d(1.5)

That means substitute x=1.5into the function:

d(1.5)=14+65(1.5)

Now multiply:

65(1.5)=97.5

Then add:

d(1.5)=14+97.5

d(1.5)=111.5

So the distance from the tower to the object at 1.5seconds is:

111.5 " meters "

The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward-opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened. The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.

This question uses a logistic function, which often models growth that starts slowly, increases rapidly, and then levels off near a maximum value. The input t represents years, and M(t) represents market share as a percent. To find when the company reaches a 60% market share, locate 60 on the vertical axis and identify where the graph reaches that height. Then read the corresponding value on the horizontal axis. From the graph, the curve reaches 60% slightly after 6 years, approximately at t=6.6. The value after 6 years is close but not yet at 60%. Therefore, the company should expect to reach 60% market share after about 6.6 years. The correct answer is D.

The graph shows weekly profit as a function of time.

The horizontal axis represents:

" years since opening "

The vertical axis represents:

" weekly profit in hundreds of dollars "

The graph is an upward-opening curve, so its minimum value occurs at the lowest point, called the vertex.

From the graph, the lowest point occurs at approximately:

t=6

So the minimum weekly profit happened approximately:

6 " years after opening "

The vertical value at this point is approximately:

9.9

Since the profit is measured in hundreds of dollars:

9.9×100=990

So the minimum weekly profit was approximately:

$990

Therefore, the correct answer is:

▭ ( " A " )

The graph shows population in thousands, and the horizontal axis represents:

" years since 1995 "

Point Pis located at approximately:

x=12

Since xrepresents years since 1995:

1995+12=2007

So point Pcorresponds to the year:

2007

The instantaneous rate of change at point Pis:

3.74

Because the vertical axis is measured in thousands, this means:

3.74 " thousand animals per year "

Convert thousands to actual animals:

3.74×1000=3740

So in 2007, the population was increasing by approximately:

3,740 " animals per year "

A horizontal asymptote is a horizontal line that a graph approaches as the input increases. Horizontal lines always have equations in the form y=constant, not x=constant. In this graph, the number of client accounts decreases over time and levels off near 125 accounts. Since the graph approaches 125 on the vertical axis, the horizontal asymptote is y=125. Choices x=125 and x=550 are vertical lines, so they cannot represent horizontal asymptotes. Choice y=550 represents a higher value near the beginning of the graph, not the long-term level. Therefore, the correct equation of the horizontal asymptote is y=125, making the answer B.

This question asks for a description of concavity and rate of change on a specific interval. From d=10 to part of the interval, the elevation is increasing, but the graph becomes less steep as it approaches a local maximum. That means the elevation increases slower and slower. After the peak, the graph begins to decrease, and the downward slope becomes steeper. This means the elevation decreases faster and faster. The correct statement must describe both parts of the interval in order: first increasing at a slowing rate, then decreasing at an increasing rate. The other answer choices either reverse the behavior or describe the wrong direction of change. Therefore, the correct answer is A.

The graph shows customer visits by day.

To determine which days likely featured new releases, we should look for the days with unusually high customer counts.

From the graph:

Day 8 has about 40customers.

Day 11 also has about 40customers.

These are the highest values shown on the graph.

Since the problem says more customers show up on days when new releases are featured, the days with the highest customer counts are the most likely new-release days.

Therefore, the correct answer is:

▭ ( " D " )

The graph represents a logistic growth model for viral infections. From day 9 to day 12, the curve is moving upward, so the number of infected people is increasing. During this interval, the graph is also becoming steeper, which means the rate of increase is getting larger. When a function is increasing and its slope is increasing, the correct description is that the quantity increases faster and faster. This interval occurs before the logistic graph begins to level off near its carrying capacity. The choices involving decrease are incorrect because the graph is not going downward. The choice “increases slower and slower” would apply to a later interval where the graph flattens. Therefore, the correct answer is A.

The graph shows a logistic growth function for conference registration. From week 1 to week 7, the number of registrants is increasing because the graph rises as time moves forward. The curve also becomes steeper throughout this interval, meaning the number of registrants is increasing at a faster rate each week. In Applied Algebra, when a graph rises and its slope increases, the correct interpretation is “increases faster and faster.” The graph is not decreasing, so both decreasing options are incorrect. The graph is also not flattening during this interval, so “increases slower and slower” does not match. Therefore, the correct answer is C.

The maximum value of a polynomial graph is found at the highest point of the curve. In this problem, P(t) represents yearly profit in millions of dollars, and t represents years since opening. The graph reaches its highest point at approximately t=10.5, so the maximum yearly profit occurs about 10.5 years after opening. The vertical value at that point is about 2.25, but because the profit is measured in millions of dollars, this means 2.25 million dollars. Converting gives 2.25×1,000,000=2,250,000. Therefore, the correct interpretation must include both the correct time and the correct dollar amount. The correct answer is C.

This question asks us to interpret a graph showing cost and revenue.

In Applied Algebra, the break-even point is where:

" Revenue " = " Cost "

On a graph, this happens where the revenue line and the cost line intersect.

From the graph:

The solid blue line represents revenue.

The dashed blue line represents cost.

The break-even point occurs where these two lines cross.

Looking carefully at the graph, the two lines intersect at approximately:

x=6

The horizontal axis represents the number of units, meaning the number of down quilts sold.

So the person needs to sell about:

6 " quilts "

to break even.

After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.

The graph shows:

P(t)= " weekly profit in thousands of dollars "

where:

t= " years since opening "

The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.

To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.

From the graph, the highest point occurs between:

t=5

and

t=6

More specifically, it is approximately:

t=5.5

So the store had its maximum weekly profit approximately:

5.5 " years after opening "

The graph shows P(t), where:

t= " years since opening "

and

P(t)= " daily profit in hundreds of dollars "

The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.

From the graph, the highest point occurs at approximately:

t=9

So the maximum daily profit happened approximately:

9 " years after opening "

The vertical value at this maximum point is approximately:

P(t)=29

But the graph measures profit in hundreds of dollars, so:

29×100=2900

Therefore, the maximum daily profit was approximately:

$2,900

So the correct interpretation is:

" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "

The function f(n) gives the distance traveled by vehicle B.

The input n represents the distance traveled by vehicle A.

The problem says vehicle B travels 17 more than vehicle A. The phrase “17 more than” means we add 17 to the amount traveled by vehicle A.

So the relationship is:

f(n)=n+17

For example, if vehicle A traveled 50 miles, then vehicle B traveled:

f(50)=50+17=67

So the correct function is:

f(n)=n+17

Therefore, the correct answer is:

B

In an exponential decay model, the horizontal asymptote represents the long-term value that the function approaches as time increases. The graph shows the number of letters processed per day decreasing quickly at first and then leveling off. Since the graph approaches the horizontal line y=1000, the long-term trend is 1,000 letters per day. This does not mean the mail center immediately processes exactly 1,000 letters, but it means the model predicts the daily number will get closer and closer to 1,000 over time. The other choices either represent values too low or values from earlier parts of the graph, not the asymptote. Therefore, the correct answer is B.

This problem asks for an average yearly rate of change over a time interval. Since x represents years since 2005, the year 2013 corresponds to x=8, and the year 2015 corresponds to x=10. Use the average rate of change formula:

10−8

f(10)−f(8)

​

Evaluating the model gives f(8)=240(1.12)

8

≈594.23 and f(10)=240(1.12)

10

≈745.40. The total change is approximately 151.17 dollars over 2 years. Dividing by 2 gives about 75.59 dollars per year. Since the question asks for the average yearly rate, not the total increase, the correct answer is B.

This question asks for the cost of each additional shirt, which means we need to find the rate of change of the linear function.

On a graph, the rate of change is the slope:

" slope " = " change in total cost " / " change in number of shirts "

From the graph, two labeled points are:

(0│33)

and

(10│173)

This means:

When 0shirts are ordered, the cost is $33.

When 10shirts are ordered, the cost is $173.

Now find the slope:

m=(173-33)/(10-0)

m=140/10

m=14

So the cost increases by:

$14

for each additional shirt.

The $33represents a fixed starting cost, not the cost per shirt.

To determine which town’s population is growing faster, compare the slopes of the two lines. In a linear population model, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A and Town B both increase over time, but Town B has the larger slope. Town B grows at about 1.3 thousand people per year, while Town A grows at about 1.1 thousand people per year. Since 1.3 > 1.1, Town B’s population is increasing at a faster rate. The values 6.5 and 5.5 describe starting population amounts, not growth rates. Therefore, the correct answer is A.

The graph represents the number of user accounts over time.

The horizontal axis represents:

" Time in months "

The vertical axis represents:

" Number of user accounts "

We need to find when the number of user accounts reached:

4,500

On the vertical axis, 4,500is halfway between:

3,000

and

6,000

So we look for the point where the blue curve reaches that height.

From the graph, the curve reaches approximately 4,500user accounts at:

x≈2.0

That means the website had about 4,500user accounts after approximately:

2.0 " months "

The graph represents:

x(t)= " number of users watching a live video "

where:

t= " hours after 9:00 a.m. "

We are asked to interpret the concavity between:

t=3.2

and

t=5.7

On this interval, the graph is going downward, so the number of users is decreasing.

Also, the graph becomes steeper as it moves downward during this interval. That means the rate of decrease is becoming larger in magnitude.

In other words, the number of users is not just decreasing; it is decreasing more quickly as time passes.

So the correct interpretation is:

" The number of users is decreasing faster and faster. "

Therefore, the correct answer is:

▭ ( " C " )

The function is:

G(t)=1,600× 〖 1.31 〗 ^t

This is an exponential growth function because the base is greater than 1:

1.31 > 1

We need to find the population after 25 minutes, so substitute:

t=25

into the function:

G(25)=1,600× 〖 1.31 〗 ^25

Evaluate the exponent and multiply:

G(25)≈1,367,421.41

Since the population is a number of bacteria cells, round to the nearest whole number:

G(25)≈1,367,421

The function u(t) gives the number of units in the inventory warehouse t hours after 9:00 a.m. The expression u(8) means the value of the inventory function 8 hours after 9:00 a.m. Since 8 hours after 9:00 a.m. is 5:00 p.m., the time must be 5:00 p.m., not 10:00 a.m. Now evaluate the function: u(8)=0.21(8)

3

−4.09(8)

2

+18.89(8)+69.5. This gives approximately 66.38, which rounds to about 66 units. Therefore, the correct interpretation is that there are approximately 66 units in the inventory at 5:00 p.m.

This situation can be modeled with a linear relationship because each box has the same weight.

We are given:

4 " boxes " →116 " pounds "

and

9 " boxes " →161 " pounds "

The weight increases because more boxes are added.

First, find the change in total weight:

161-116=45

Then find the change in the number of boxes:

9-4=5

Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:

45/5=9

So each box weighs:

9 " pounds "

Check:

If each box weighs 9 pounds, then adding 5 more boxes adds:

5(9)=45

116+45=161

This matches the given information.

The graph shows an increasing exponential curve.

The number of subscribers is going up as time passes, so the function is increasing.

Also, the graph becomes steeper as time increases. This means the rate of increase is getting larger.

So the number of subscribers is:

" increasing faster and faster "

This is a key feature of exponential growth.

The average rate of change measures how much the output changes per one unit of input.

Here:

t= " hours after 8:00 a.m. "

and

n(t)= " number of people at the park "

The two given points are:

A=(2,110)

and

B=(6,182)

This means:

At t=2hours after 8:00 a.m., there were 110people at the park.

At t=6hours after 8:00 a.m., there were 182people at the park.

Now calculate the average rate of change:

" Average rate of change " =(182-110)/(6-2)

=72/4

=18

Because the value is positive, the number of people is increasing.

So the correct interpretation is:

" The number of people at the park increases at an average rate of 18 people per hour. "

This is an exponential growth problem because the base 1.13 is greater than 1. The function starts with 2,900 bacteria and grows by a factor of 1.13 each hour, which represents a 13% hourly increase. To find the population after 18 hours, substitute t=18 into the function: f(18)=2900(1.13)

18

Evaluating the exponent and multiplying by 2900 gives approximately 26,170.38. Since bacteria are counted as whole organisms, this rounds to about 26,170 bacteria. The other answer choices do not match the exponential model at t=18. Therefore, the correct answer is C.

This question asks us to identify a correct conclusion from the graph.

The vertical axis represents:

" number of daily homework problems "

The horizontal axis represents:

" school days since the beginning of the term "

From the graph, the lowest point occurs at the far right, around:

" day " 22

The corresponding number of homework problems is approximately:

18

So the minimum number of daily homework problems is 18, and it occurs at day 22.

Therefore, the correct answer is:

▭ ( " D " )