Authentic WGU Certification Exam Applied-Algebra Questions 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