The WGU Applied Algebra FXO2 PFXP C957 (Applied-Algebra)

A logistic function often increases quickly in the middle and then begins to level off as it approaches a maximum carrying capacity. From year 7 to year 10, the graph is still increasing, so the bison population is going up. However, the curve is becoming flatter during this interval. A flatter curve means the slope is getting smaller, so the population is increasing at a slower rate. This behavior is described as “increases slower and slower.” It is not decreasing, because the graph continues to move upward. It is also not increasing faster and faster, because the slope is not becoming steeper in this interval. Therefore, the correct interpretation is answer B.

The graph shows the value of the coin increasing over time. Since the curve rises from left to right, the value is not decreasing. The graph also becomes steeper as time increases, which means the rate of increase is getting larger. In Applied Algebra, when a graph is increasing and its slope is increasing, the quantity is described as increasing faster and faster. This is typical of exponential growth, where values grow by a repeated percent or factor rather than by a constant amount. The choices involving decreasing are incorrect because the graph moves upward. The choice “increasing slower and slower” would require the graph to flatten, which it does not. 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 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:

W(x)=740× 〖 0.87 〗 ^x

This is an exponential decay function because the base 0.87is between 0 and 1:

0 < 0.87 < 1

That means the sample’s weight decreases over time.

We need to find the weight when:

x=3

Substitute 3into the function:

W(3)=740× 〖 0.87 〗 ^3

First calculate the exponent:

〖 0.87 〗 ^3=0.87×0.87×0.87

〖 0.87 〗 ^3=0.658503

Now multiply by 740:

W(3)=740×0.658503

W(3)=487.29222

Rounded to two decimal places:

W(3)≈487.29

So the weight of the radioactive sample after 3 years is approximately:

487.29 " oz. "

This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase “2 more than” tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has 10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.

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

Key behavior of logistic functions:

Initial phase (early time) → growth is slow

Middle phase → growth speeds up (increasing rate)

Later phase → growth slows down as it approaches a maximum

Analyze the interval from day 1 to day 17:

This interval is in the early part of the graph.

The curve is increasing and getting steeper over this range.

That means the rate of increase is growing over time.

So, the number of comments is:

" increasing faster and faster "

The function is:

f(x)=190× 〖 0.99 〗 ^x

Since xrepresents the number of years since 2003:

2012 ⇒ x=9

2015 ⇒ x=12

The average rate of change from 2012 to 2015 is:

(f(12)-f(9))/(12-9)

First, find f(9):

f(9)=190× 〖 0.99 〗 ^9

f(9)≈173.59

Now find f(12):

f(12)=190× 〖 0.99 〗 ^12

f(12)≈168.37

Now calculate the average rate of change:

(168.37-173.59)/(12-9)

=(-5.22)/3

≈-1.74

Rounded to the nearest whole number:

-2

The negative sign means the number of subscribers is decreasing.

So the correct interpretation is:

" The number of subscribers decreases at an average rate of about 2 subscribers per year. "

The graph represents:

p(t)= " number of people at the gym "

where:

t= " hours after 7:00 a.m. "

The question asks about the concavity of the graph between:

t=1.3

and

t=3.4

On this interval, the graph is still going upward, so the number of people is increasing.

However, the graph is beginning to flatten as it approaches its highest point. That means the slope is positive, but the slope is getting smaller.

In other words:

" The number of people is increasing, but at a slower rate. "

This is called concave down behavior. For a concave down graph that is increasing, the correct interpretation is:

" increasing slower and slower "

Therefore, the correct answer is:

▭ ( " C " )