Q: A $$1000 investment earns 1.5% annual interest, compounded quarterly, for 10 years. Which formula gives the final amount A$?

$$A = 1000 \left(1 + \frac{0.015}{4}\$$right)^{4 \times 10}$$

Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = a^x$$ where $$a \u003e 1$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 2

Given the function $$f(x) = 3^x$$, which of the following points lies on its graph?

Accepted Answer

$$(0, 1)$$

Question 3

Which property of exponents is used to simplify $$\left(a^m\right)^n$$?

Accepted Answer

$$a^{mn}$$

Question 4

If $$f(x) = a^x$$ with $$0 \u003c a \u003c 1$$, which of the following statements is true about its graph?

Accepted Answer

The function is decreasing and continuous on $$(-\infty, \infty)$$

Question 5

Which of the following is equivalent to $$\frac{2$$^{2x+3}$$}{3$$^{4t-4}$$}$$?

Accepted Answer

$$2^{2x+3}$$ \cdot $$3^{-(4t-4)}$$

Question 6

Solve for $$x$$: $$25^x = 125.$$

Accepted Answer

$$x = \frac{3}{2}$$

Question 7

Which of the following best describes the horizontal asymptote of $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

The x-axis ($$y = 0)$$

Question 8

If $$f(x) = 2^x$$ and $$g(x) = -2^x$$, how does the graph of $$g(x)$$ relate to $$f(x)$$?

Accepted Answer

It is a reflection of $$f(x)$$ across the x-axis

Question 9

A $$1000 investment earns 1.5% annual interest, compounded quarterly, for 10 years. Which formula gives the final amount A$?

Accepted Answer

$$A = 1000 \left(1 + \frac{0.015}{4}\$$right)^{4 	imes 10}$$

Question 10

What is the value of $$e to $$eleven decimal places?

Accepted Answer

$$2.71828182846$$

Question 11

Which formula should be used to calculate the amount $$A$$ after $$t$$ years if $$P$$ dollars are invested at an annual rate $$r$$ compounded continuously?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 12

Suppose $$f(x) = r(1.11)^x$$ models the risk of heart disease after age 40. If $$r = 0.02$$, what is the risk at age 75?

Accepted Answer

$$0.02 	imes (1.11$$)^{35}$$

Question 13

Solve for $$x$$: $$3^{x+5} = 9^x$.

Accepted Answer

$$x = -5$$

Question 14

Which of the following is the correct simplification of $$2^{-3y}$$?

Accepted Answer

$$\frac{1}{2$$^{3y}$$}$$

Question 15

If $$A = P(1 + r)^n$$, what does $$n$$ represent in the context of compound interest?

Accepted Answer

The number of compounding periods

Question 16

Solve the inequality $$32^x \u003c 81$$ for $$x.$$

Accepted Answer

$$x \u003c \frac{4}{5}$$

Question 17

Which of the following is the correct solution to $$6^{2x+3} = 1$?

Accepted Answer

$$x = -\frac{3}{2}$$

Question 18

Which of the following best describes the behavior of $$f(x) = a^x as$$ $$x 	o -\infty$$ for $$a \u003e 1$$?

Accepted Answer

$$f(x) 	o 0$$

Exponential Functions and Their Applications

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