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

This is an exponential growth problem because the base 1.13 is greater than 1. The function starts with 2,900 bacteria and grows by a factor of 1.13 each hour, which represents a 13% hourly increase. To find the population after 18 hours, substitute t=18 into the function: f(18)=2900(1.13)

18

Evaluating the exponent and multiplying by 2900 gives approximately 26,170.38. Since bacteria are counted as whole organisms, this rounds to about 26,170 bacteria. The other answer choices do not match the exponential model at t=18. Therefore, the correct answer is C.

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 graph shows the weekly number of players on a gaming website.

The horizontal axis represents:

" years since launching "

The vertical axis represents:

" players in hundreds "

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

From the graph, the lowest point occurs at approximately:

t=4

This means the website reached its minimum weekly number of players approximately:

4 " years after it was launched "

Therefore, the correct answer is:

▭ ( " B " )

The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward-opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened. The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.

This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139−39=100 dollars. Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.

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This question asks which town’s population is growing at a faster rate.

Since both population graphs are straight lines, we compare their slopes.

The slope of a line represents the rate of change:

" slope " = " change in population " / " change in time "

From the graph:

Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.

Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.

Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.

Compare the rates:

1.3 > 1.0

So Town B is growing faster than Town A.

This question asks us to interpret a graph showing cost and revenue.

In Applied Algebra, the break-even point is where:

" Revenue " = " Cost "

On a graph, this happens where the revenue line and the cost line intersect.

From the graph:

The solid blue line represents revenue.

The dashed blue line represents cost.

The break-even point occurs where these two lines cross.

Looking carefully at the graph, the two lines intersect at approximately:

x=6

The horizontal axis represents the number of units, meaning the number of down quilts sold.

So the person needs to sell about:

6 " quilts "

to break even.

After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.

This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions. Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.

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 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 " )