Question 1

Based on the graph showing the percent of students in the College of Engineering at Stale University, which of the following statements is true about the function represented by the graph?

Accepted Answer

The graph represents a function because each year corresponds to exactly one percentage.

Question 2

Refer to the graph of percent of students in the College of Engineering. What is the value of $$f(1995)$$?

Accepted Answer

$$f(1995) = 18\%$$

Question 3

If $$f(x) = 12\% in $$the graph of percent of students in the College of Engineering, what year does $$x$$ represent?

Accepted Answer

$$x = 1980$$

Question 4

Given the function $$f(x) = \frac{2x-3}{x+6}$$, what is $$f(-1)$$?

Accepted Answer

$$f(-1) = \frac{-5}{5}$$

Question 5

Find and simplify the difference quotient for $$f(x) = 7x - 4.$$

Accepted Answer

$$\frac{f(x+h)-f(x)}{h} = 7$$

Question 6

Write the equation of the line passing through $$(3,5)$$ and $$(-5,6) in $$point-slope form.

Accepted Answer

$$y - 5 = -\frac{1}{8}(x - 3)$$

Question 7

A car's value depreciates from $$14,760 in 1991 to 4$$,440 in 1994$$. Let y$ be the value in year x$, where x=0$ is 1991. What is the linear equation modeling the value?

Accepted Answer

$$y = -4,106.67x + 14,760$$

Question 8

Find the average rate of change of $$f(x) = x^2$ from x = 2$ to x = 8$.

Accepted Answer

$$12$$

Question 9

You inherit $$10,000$$ and must invest in two stocks at $$6\%$$ and $$11\%$$ annual interest. If the total interest earned is $$900$$, how much should be invested at $$6\%$$?

Accepted Answer

$$4,400$$

Question 10

A rectangular room's length is $$7$$ feet longer than twice its width. If the perimeter is $$194$$ feet, what is the width?

Accepted Answer

$$27$$ feet

Question 11

A ladder $$10$$ feet long is $$6$$ feet from the base of a wall. How far up the wall does the ladder reach?

Accepted Answer

$$8$$ feet

Question 12

You have $$600$$ feet of fencing to enclose a rectangular plot bordering a river (no fence along the river). What is the maximum area that can be enclosed?

Accepted Answer

$$45,000$$ square feet

Question 13

Solve the equation $$8x^2 - 5x = 9x - 36$.

Accepted Answer

$$x = 4$$, $$x = -1.5$$

Question 14

For the function $$f(x) = \frac{24,000 + 280x}{x}$$, how many units must be produced for the average cost per unit to be $$440$$?

Accepted Answer

$$60$$ units

Question 15

A city grows at $$0.8\%$$ annually. If there were $$3,980,000$$ residents in $$1995$$, how many are there in $$2000$$? Use $$y = 3,980,000(2.7$$)^{0.008t}$$, where t$ is years since 1995$.

Accepted Answer

$$4,140,000$$

College Algebra Final Exam Review – Step-by-Step Guidance

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