Pass the WGU Courses and Certificates Applied-Algebra Questions and answers with CertsForce

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:

▭ ( " D " )

The function c(t)gives the number of active shopping carts on a website.

Because c(t)represents active carts, the difference between c(6)and c(8)will be measured in:

" active carts "

not hours.

First evaluate c(6):

c(6)=-0.01(6)^4+0.25(6)^3-2.33(6)^2+9.02(6)+8

c(6)=19.28

Now evaluate c(8):

c(8)=-0.01(8)^4+0.25(8)^3-2.33(8)^2+9.02(8)+8

c(8)=18.08

Now find the difference:

19.28-18.08=1.20

This is approximately:

1 " active cart "

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 problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship. Day 12 also does not match the main peaks. Therefore, the correct answer is C.

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

The horizontal axis represents:

" days "

The vertical axis represents:

" widgets "

The graph gives two labeled points:

(6│3.4)

and

(14│23)

The average rate of change is:

" change in widgets " / " change in days "

Substitute the values:

(23-3.4)/(14-6)

=19.6/8

=2.45

Rounded to the nearest tenth:

2.5

This means the team increased production by an average of approximately:

2.5 " widgets each day "

Therefore, the correct answer is:

▭ ( " B " )

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 "

The average rate of change measures how much the output changes per one unit of input. Here, the input is time in hours after 6:00 a.m., and the output is the number of vehicles stopped at the toll booth. The two given points are A=(1,49.4) and B=(4,45.8). Use the average rate of change formula: (y

2

​

−y

1

​

)/(x

2

​

−x

1

​

). Substituting the coordinates gives (45.8−49.4)/(4−1). The numerator is −3.6, and the denominator is 3, so the average rate of change is −1.2. The negative sign means the number of vehicles decreased over the interval.

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:

▭ ( " A " )

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.