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

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 regression function has:

r^2=0.54

This indicates a moderate fit, not a strong fit. The model explains some of the variation in the data, but not as strongly as a model with an r^2value closer to 1.

Now consider the prediction at:

x=20.6

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

x=18

The prediction at x=20.6is beyond the observed data, so it is an extrapolation. However, it is not very far beyond the data range.

Because x=20.6is within a reasonable extrapolation range and the model has a moderate fit, the prediction is appropriate.

The graph shows a linear relationship between:

" Number of boards "

and

" Total cost "

The cost of each additional board is the rate of change, or slope, of the line.

From the graph, two labeled points are:

(0│27)

and

(10│177)

This means:

When 0 boards are ordered, the total cost is $27.

When 10 boards are ordered, the total cost is $177.

Now calculate the slope:

m=(177-27)/(10-0)

m=150/10

m=15

So each additional board costs:

$15

Therefore, the correct answer is:

▭ ( " B " )

From week 1 to week 7, the graph is increasing and becoming steeper.

In Applied Algebra, when a graph is increasing and its slope is getting larger, the quantity is said to be:

" increasing faster and faster "

This interval is on the early increasing part of the logistic curve, before the graph begins to level off.

Therefore, the correct answer is:

▭ ( " B " )

The graph shows weekly profit as a function of time.

The horizontal axis represents:

" years since opening "

The vertical axis represents:

" weekly profit in hundreds of dollars "

The graph is an upward-opening curve, so its minimum value occurs at the lowest point, called the vertex.

From the graph, the lowest point occurs at approximately:

t=6

So the minimum weekly profit happened approximately:

6 " years after opening "

The vertical value at this point is approximately:

9.9

Since the profit is measured in hundreds of dollars:

9.9×100=990

So the minimum weekly profit was approximately:

$990

Therefore, the correct answer is:

▭ ( " A " )

The graph shows a linear relationship between:

w= " water in cups "

and

l= " lemon juice in cups "

The line passes through the origin, so the relationship has the form:

l=mw

where mis the rate of change.

From the graph, a clear point on the line is approximately:

(8│5)

This means when there are 8 cups of water, there are 5 cups of lemon juice.

The rate of change is:

m= " change in lemon juice " / " change in water "

m=5/8

So the relationship is:

l=5/8 w

This means the amount of lemon juice must be:

5/8

of the amount of water.

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 " )

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

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 "

The graph shows a decreasing exponential model.

The vertical axis represents:

" Licensed sellers "

The horizontal axis represents:

" Time in years "

The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:

y=100

That horizontal line is the horizontal asymptote.

A horizontal asymptote represents the long-term value the function approaches as time continues.

So the correct interpretation is:

" In the long run, the number of licensed sellers nears 100. "

Therefore, the correct answer is:

▭ ( " C " )