Question 1

A savings account is opened with $$4,000 and earns 2.75% interest compounded semi-annually. Which formula correctly models the amount A$ in the account after t$ years?

Accepted Answer

$$A = 4000(1 + 0.0275/2$$)^{2t}$$

Question 2

Given the function $$f(x) = -3x^2$ - 11x + 17$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = -3(-2)^2$ - 11(-2) + 17 = -12 + 22 + 17 = 27$$

Question 3

Which of the following is the correct way to write $$\log_2$ 2x - \log_2$ y + 3 \log_2$ x as a $$single logarithm?

Accepted Answer

$$\log_2$ \left( \dfrac{2x^4$}{y} \right)$$

Question 4

Suppose the demand function for a product is $$p = \dfrac{80}{q+2}$$, where $$q is $$the number of units demanded and $$p is $$the price per unit. How many units will be demanded if the price is $$61.71$$ per unit?

Accepted Answer

$$q = 1$$

Question 5

Given the quadratic equation $$3x^2 + 16x - 35 = 0$, which of the following is the correct factorization?

Accepted Answer

$$(3x - 5)(x + 7) = 0$$

Question 6

Let $$g(x) = 5^x. $$What is the y-intercept of the graph of $$g$$?

Accepted Answer

$$(0, 1)$$

Question 7

Which of the following statements about logarithms is correct?

Accepted Answer

A logarithm is an exponent.

Question 8

Given $$f(x) = x^2$ - 6x + 8$$, what are the vertex and the direction of opening?

Accepted Answer

Vertex: $$(3, -1)$$, opens up

Question 9

Which of the following is the correct exponential form for $$\log_3$ 256 = x$$?

Accepted Answer

$$3^x = 256$$

Question 10

Given the function $$g(x) = 2 - \sqrt{3 - 2x}$$, what is the domain of $$g in $$interval notation?

Accepted Answer

$$(-\infty, \dfrac{3}{2}]$$

Question 11

If $$M(t) = -16t^2$ + 12t + 200$$ models the height of a phone dropped from a cliff, how long until the phone hits the ground?

Accepted Answer

$$t = 3.75$$

Question 12

Which of the following is the correct equation, in slope-intercept form, for the line passing through $$(-6,4)$$ with slope $$\frac{1}{2}$$?

Accepted Answer

$$y = \frac{1}{2}x + 7$$

Question 13

Given $$f(x) = \dfrac{2x+5}{x^2$-1}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, 1) \cup (1, \infty)$$

Question 14

Which of the following is the correct solution to $$6(4^{x-3}) = 120$?

Accepted Answer

$$x = 4$$

Question 15

If $$D(t) = 321t + 6,321$$ models the total disposable income in billions of dollars, what does the slope represent?

Accepted Answer

The annual increase in disposable income (in billions of dollars)

Question 16

Which of the following is the correct solution to $$\ln x + 3 = \ln(x + 4)$$?

Accepted Answer

$$x = 2$$

Question 17

Given the points $$(11, -2)$$ and $$(-3, 7)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = -\dfrac{9}{14}$$

Question 18

Which of the following is the correct solution to $$4096 = 8^x$$?

Accepted Answer

$$x = 8$$

Question 19

Which of the following is the correct equation for the population of quail, starting at 851 and increasing at 2.5% per year?

Accepted Answer

$$N(t) = 851(1.025)^t$$

College Algebra Final Exam Review: Key Concepts and Practice Problems

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