Applied-Algebra Exam Dumps - WGU Courses and Certificates Questions and Answers

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 is a logistic growth function.

A logistic function often has an S-shape. It begins by increasing slowly, then increases faster and faster, and later levels off as it approaches a maximum carrying capacity.

From year 1 to year 9, the graph is rising and becoming steeper.

That means:

" the wild horse population is increasing "

and the slope is getting larger, so:

" the population is increasing faster and faster "

Therefore, the correct answer is:

▭ ( " 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 average rate of change tells how much the output changes per one unit of input.

Here:

t= " hours after 5:00 a.m. "

and

n(t)= " number of animals "

The two given points are:

A=(1,10.6)

and

B=(8,6.59)

Use the average rate of change formula:

(y_2-y_1)/(x_2-x_1 )

Substitute the coordinates:

(6.59-10.6)/(8-1)

=(-4.01)/7

≈-0.573

The negative sign means the number of animals is decreasing.

So the correct interpretation is:

" The number of animals at the station decreases at an average rate of " 0.573 " animals per hour. "

Therefore, the correct answer is:

▭ ( " B " )

The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:

C(t)=mt+b

where:

m= " hourly rate "

and

b= " flat rate "

We are given two points:

(3│220)

and

(5│340)

These mean:

A 3-hour job costs $220.

A 5-hour job costs $340.

First, find the hourly rate using slope:

m=(340-220)/(5-3)

m=120/2

m=60

So the contractor charges:

$60 " per hour "

Now the function has the form:

C(t)=60t+b

Use the point (3│220)to find the flat rate:

220=60(3)+b

220=180+b

b=40

So the function is:

C(t)=60t+40

Check with t=5:

C(5)=60(5)+40

C(5)=300+40

C(5)=340

This matches the given information.

The graph shows the water volume decreasing over time.

The vertical axis represents:

" Water volume in gallons "

The horizontal axis represents:

" Time in minutes "

The graph is an exponential decay curve. It decreases quickly at first, then levels off.

From the graph, the curve approaches a horizontal value near:

y=1,000

This means the horizontal asymptote is approximately:

y=1,000

Since the graph approaches 1,000 gallons, it will not decrease to 500 gallons according to this model.

The water volume does not change by a constant rate because exponential functions do not have constant additive change. Also, the graph decreases fastest at the beginning, not later.

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

The value

r^2=0.96

indicates a strong fit because it is very close to 1. This means the regression model explains much of the variation in the traffic-frequency data.

However, we also need to check whether the prediction at

x=16.2

is a reasonable extrapolation.

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

x=14

The predicted value is slightly beyond the observed data range, but not extremely far beyond it.

Since x=16.2is still within a reasonable extrapolation range, and the model has a strong r^2value, the prediction is appropriate.

Therefore, the correct answer is:

▭ ( " C " )

The graph shows a decreasing exponential function.

The vertical axis represents:

" Letters per day "

The horizontal axis represents:

" Time in years "

For an exponential decay graph, the value decreases quickly at first and then begins to level off. The value it approaches in the long run is called the horizontal asymptote.

From the graph, the curve levels off near:

y=2,500

So the number of letters processed per day is trending toward:

2,500

This does not mean the mail center immediately processes exactly 2,500 letters per day. It means that as time continues, the number gets closer and closer to 2,500.

Therefore, the correct answer is:

▭ ( " B " )

The function V(t)represents the number of travelers in the travel depot.

The input trepresents:

" hours after 7:00 a.m. "

The output V(t)represents:

" number of travelers "

So V(2)means the number of travelers in the depot:

2 " hours after 7:00 a.m. "

From the graph, when:

t=2

the value of V(t)is approximately:

79.2

Since V(t)measures travelers, not hours, V(2)represents:

79.2 " travelers "

Therefore, the correct answer is:

▭ ( " D " )