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

The table gives the percent of customers with fiber internet for each year since 2020.

Since 2023 is:

2023−2020=3

we use the row where:

Years since 2020=3

From the table, the percent of customers with fiber internet in 2023 is:

57%

The company has approximately:

1,050

customers each year.

Now find 57% of 1,050:

0.57×1,050=598.5

The closest answer choice is:

598

So approximately 598 customers had fiber internet in 2023.

Therefore, the correct answer is:

C

The graph shows a decreasing exponential function.

In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote.

The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.

From the graph, the curve decreases quickly at first, then begins to level off near:

y=1,000

This means that as time continues, the number of letters processed per day approaches:

1,000

So the long-term trend is that the mail center will process about:

1,000 " letters per day "

This question asks which town’s population is growing at a faster rate.

Since both population graphs are straight lines, we compare their slopes.

The slope of a line represents the rate of change:

" slope " = " change in population " / " change in time "

From the graph:

Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.

Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.

Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.

Compare the rates:

1.3 > 1.0

So Town B is growing faster than Town A.

The function is:

f(x)=1,300× 〖 0.92 〗 ^x

This is an exponential decay function because the base is between 0 and 1:

0 < 0.92 < 1

So the number of registered voters is decreasing over time.

Since xrepresents the number of years since 2001:

2001 ⇒ x=0

2007 ⇒ x=6

2008 ⇒ x=7

2009 ⇒ x=8

2012 ⇒ x=11

2021 ⇒ x=20

To determine the fastest average decrease, compare the average rates of change. A faster decrease means the average rate of change is more negative.

For 2001 to 2007:

(f(6)-f(0))/(6-0)

f(0)=1300

f(6)=1300(0.92)^6≈788.31

(788.31-1300)/6≈-85.28

So from 2001 to 2007, the number of registered voters decreased by about:

85.28 " voters per year "

For 2007 to 2008:

(f(7)-f(6))/(7-6)≈-63.06

For 2008 to 2021:

(f(20)-f(7))/(20-7)≈-42.58

For 2009 to 2012:

(f(11)-f(8))/(11-8)≈-45.13

Now compare the decreases:

-85.28, -63.06, -42.58, -45.13

The most negative rate is:

-85.28

That means the fastest average decrease happened from:

2001 " to " 2007

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

The horizontal axis represents:

" Time in minutes "

The vertical axis represents:

" Temperature in degrees Fahrenheit "

The curve decreases and approaches the horizontal axis as time increases.

A horizontal asymptote is a horizontal line that the graph approaches but may not reach. Horizontal lines have equations of the form:

y= " constant "

From the graph, the curve approaches:

y=0

So the horizontal asymptote is:

y=0

The options x=0and x=500are vertical lines, not horizontal asymptotes.

Therefore, the correct answer is:

â–­ ( " B " )

The graph shows a logistic regression model for rabbit population data.

The given value is:

r^2=0.94

An r^2value close to 1means the model fits the data well. Since 0.94is close to 1, the regression model is a strong fit.

However, extrapolation should still be done carefully. Extrapolation means using the model to predict values outside the observed data range.

From the scatterplot, the data values appear to run roughly from about:

x=4 " to " x=20

A reasonable extrapolation range should stay close to the observed data. The interval:

x=0 " to " x=24

extends slightly beyond the data on both sides, so it is more reasonable than the much wider interval:

x=-4 " to " x=28

The statements saying extrapolation is not appropriate because r^2 < 1or because r^2 > 0.7are not valid interpretations.

The graph compares the spread of two viruses over time.

The horizontal axis represents:

" time in months "

The vertical axis represents:

" percent of the population affected "

The graph shows:

Virus A as the solid blue curve.

Virus B as the dashed blue curve.

To determine which statement is correct, compare when each virus reaches the same population percentage.

At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.

However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.

So the correct conclusion is:

" Virus A affects " 20% " of the population before virus B does. "

Therefore, the correct answer is:

â–­ ( " A " )

The function w(t)gives the number of workers at the job site thours after 6:00 a.m.

We need to find the difference between:

w(4)

and

w(8)

Because w(t)represents workers, the difference will be measured in workers, not hours.

First, evaluate w(4):

w(4)=0.03(4)^4-0.81(4)^3+7.55(4)^2-26.62(4)+44

w(4)=0.03(256)-0.81(64)+7.55(16)-106.48+44

w(4)=7.68-51.84+120.8-106.48+44

w(4)=14.16

Now evaluate w(8):

w(8)=0.03(8)^4-0.81(8)^3+7.55(8)^2-26.62(8)+44

w(8)=0.03(4096)-0.81(512)+7.55(64)-212.96+44

w(8)=122.88-414.72+483.2-212.96+44

w(8)=22.4

Now find the difference:

22.4-14.16=8.24

This is approximately:

8 " workers "

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.

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.

This graph represents a logistic growth function, which has an S-shaped curve:

Slow growth at the beginning (near point A)

Rapid growth in the middle (near point B and C)

Slowing growth at the end (near point D)

Key Concept:

Instantaneous rate of change = slope of the tangent line at a single point

Average rate of change = slope between two points

Analyze the graph:

At point A → slope is small (slow increase)

From A to C → increasing but not maximum

At point C → curve is steepest → maximum slope

From C to D → curve flattens → smaller slope

At point D → slope is very small (almost flat)

Conclusion:

The greatest rate of change occurs where the graph is steepest, which is at:

" Point C "

This question is about reading an ordered pair from a graph.

An ordered pair has the form:

(x│y)

where:

x= " time in hours "

and

y= " audience size "

From the graph:

Point Ais at approximately (0│402)

Point Bis at (2│401)

Point Cis at (4│403)

Point Dis at (6│406)

Point Eis at approximately (8│410)

Point Fis at (10│408)

Now compare these graph points with the answer choices.

Choice A says:

(2│401)

This matches point Bon the graph exactly.

The other choices do not match the graph:

(4│404)

is incorrect because at x=4, the graph shows about 403, not 404.

(8│409)

is incorrect because at x=8, the graph is about 410, not 409.

(10│407)

is incorrect because at x=10, the graph shows about 408, not 407.

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.

The function a(x)represents the total value of an investment account.

The horizontal axis represents:

x= " time in years "

The vertical axis represents:

a(x)= " total account value in dollars "

We are asked to find the total value when:

x=4

To answer this from the graph:

Locate x=4on the horizontal axis.

Move vertically upward until reaching the blue graph.

Read the corresponding value on the vertical axis.

From the graph, when x=4, the value is slightly above $1,800, approximately:

a(4)≈1,830.59

So the total value of the investment account after 4 years is approximately:

$1,830.59

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:

â–­ ( " D " )

We are told that computer B completes 12 more tasks than computer A.

Let:

x= " number of tasks completed by computer A "

and

F(x)= " number of tasks completed by computer B "

The phrase “12 more than” means add 12 to the original amount:

F(x)=x+12

So, if computer A completes xtasks, computer B completes:

x+12

tasks.

For example, if computer A completed 50 tasks, then computer B completed:

F(50)=50+12=62

Therefore, the correct answer is:

â–­ ( " B " )

The function is:

P(t)=462-35t

This is a linear function in the form:

P(t)=mt+b

where:

m= " rate of change "

and

b= " initial value "

In this function:

m=-35

The negative sign means the fish population is decreasing.

The number 35tells us the amount of decrease per month.

So the fish population is decreasing by:

35 " fish per month "

The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:

P(0)=462

Therefore, the correct interpretation is:

" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. "

So the correct answer is:

â–­ ( " D " )

The graph is a logistic growth curve.

A logistic growth curve has two main concavity regions:

" concave up before the inflection point "

and

" concave down after the inflection point "

From the graph, the function increases faster and faster until about:

x=6

After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.

This is concave down behavior.

Therefore, one interval where the graph is concave down is:

(6│11)

So the correct answer is:

â–­ ( " D " )

The function is:

p(m)=5m+5

This is a linear function in the form:

p(m)=mx+b

For a linear function, the average rate of change over any interval is the same as the slope.

The slope is the coefficient of m:

5

So the price increases at a constant rate of:

$5 " per month "

We can also verify using the average rate of change formula:

(p(10)-p(1))/(10-1)

Find p(10):

p(10)=5(10)+5=55

Find p(1):

p(1)=5(1)+5=10

Now calculate:

(55-10)/(10-1)

=45/9

=5

Since xrepresents the number of years since 2004:

2013-2004=9

so:

2013 ⇒ x=9

Also:

2018-2004=14

so:

2018 ⇒ x=14

The average yearly rate of change from 2013 to 2018 is:

(f(14)-f(9))/(14-9)

Now evaluate the function:

f(9)=330× 〖 1.04 〗 ^9

f(9)≈469.37

f(14)=330× 〖 1.04 〗 ^14

f(14)≈571.13

Now calculate the average rate of change:

(571.13-469.37)/5

=101.76/5

=20.35

So the painting’s value increased by an average of about:

$20.35 " per year "

Therefore, the correct answer is:

â–­ ( " A " )

The graph shows the queue size changing over time.

The horizontal axis represents:

" Time in minutes "

The vertical axis represents:

" Queue size "

The graph is a decreasing exponential curve. It starts near 750people and decreases quickly at first. Then the curve begins to flatten near:

y=100

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

Here, the graph approaches the horizontal line:

y=100

This means that as time passes, the number of people in the virtual queue gets closer and closer to 100.

It does not mean the queue decreases to 0, because the graph levels off near 100, not near 0.

Therefore, the correct interpretation is:

" As time passes, the number of people in the queue approaches 100. "

From d=0to about d=2, the graph is decreasing, but it is flattening as it approaches a minimum. This means the number of raffle tickets sold is decreasing at a slower rate:

" decreases slower and slower "

After the minimum, from about d=2to d=4.4, the graph increases and becomes steeper. This means the number of raffle tickets sold is increasing at a faster rate:

" increases faster and faster "

So the correct description is:

" The number of raffle tickets decreases slower and slower and then increases faster and faster. "

We need to compare the two account values after:

t=3

First, find the value of Account 1:

A_1 (3)=6,500× 〖 1.05 〗 ^3

A_1 (3)=6,500×1.157625

A_1 (3)≈7,524.56

Now find the value of Account 2:

A_2 (3)=3,000× 〖 0.96 〗 ^3

A_2 (3)=3,000×0.884736

A_2 (3)≈2,654.21

Now subtract:

7,524.56-2,654.21=4,870.35

So Account 1 is about:

$4,870

greater than Account 2 after 3 years.

Therefore, the correct answer is:

â–­ ( " C " )

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

The horizontal axis represents:

Days

The vertical axis represents:

Practice duration in minutes

We need to find the practice duration on day 8.

To do this:

Locate 8 on the horizontal axis.

Move vertically until you reach the blue graph.

Read the corresponding value on the vertical axis.

From the graph, when:

x=8

the blue graph is at:

y=115

So the musician practiced for:

115 minutes

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