Q: For the same investment, what is the formula for the future value if compounded continuously?

$$A = 8000 e$$^{0.03 \times 11}$$

Question 1

Given the piecewise function $$f(x) = \begin{cases} 3x - 2, & x \u003c 0 \ x^2$, & x \geq 0 \end{cases}$$, which of the following statements is TRUE about the graph of $$f(x)$$?

Accepted Answer

The graph has a jump discontinuity at $$x = 0.$$

Question 2

Find the inverse function $$f^{-1}(x$$)$$ for f(x) = 2$$ - \frac{1}{x}$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{2 - x}$$

Question 3

What is the range of the inverse function $$f^{-1}(x$$)$$ for f(x) = 2$$ - \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 4

For $$f(x) = \log_2$(x + 1)$$, what is the domain of $$f$$?

Accepted Answer

$$(-1, \infty)$$

Question 5

Evaluate $$f(0)$$ for $$f(x) = \log_2$(x + 1).$$

Accepted Answer

$$0$$

Question 6

Which of the following best describes the range of $$f(x) = \log_2$(x + 1)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 7

If $$y = f(x) is $$graphed, how is the graph of $$y = f$$^{-1}$$(x)$$ related to it?

Accepted Answer

It is the reflection of $$y = f(x)$$ across the line $$y = x.$$

Question 8

Solve for $$x$$: $$(16)^{2x+1}$$ = $$8^{x-4}.$$

Accepted Answer

$$x = -5$$

Question 9

Solve for $$x$$: $$3 \ln(x + 1) = 2.$$

Accepted Answer

$$x = e$$^{2/3}$$ - 1$$

Question 10

Solve for $$x$$: $$\log_8$(x + 3) + \log_8$(x + 5) = \log_8$(15).$$

Accepted Answer

$$x = 1$$

Question 11

A patient’s medication concentration in the bloodstream is modeled by $$C(t) = C_0$ e$$^{-kt}$$, where C_0$ is the initial concentration and k$ is a positive constant. If the concentration halves every 4 hours, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{4}$$

Question 12

If $$8,000 is invested for 11 years at 3% interest compounded quarterly, what is the future value? (Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$)

Accepted Answer

$$A = 8000 \left(1 + \frac{0.03}{4}\$$right)^{44}$$

Question 13

For the same investment, what is the formula for the future value if compounded monthly?

Accepted Answer

$$A = 8000 \left(1 + \frac{0.03}{12}\$$right)^{132}$$

Question 14

For the same investment, what is the formula for the future value if compounded continuously?

Accepted Answer

$$A = 8000 e$$^{0.03 	imes 11}$$

Question 15

A chemical reaction’s rate is modeled by $$R(t) = R_0$ e$$^{-kt}$$. If the rate drops to 25% of its initial value after 10 minutes, what is k$?

Accepted Answer

$$k = \frac{\ln 4}{10}$$

Question 16

Which of the following is the correct domain for the function $$f(x) = 2 - \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 17

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$[0, \infty)$$

Question 18

A population grows according to $$P(t) = 5000 e$$^{0.02t}$$. How long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.02}$$

Question 19

Which of the following is the correct solution for $$x$$ such that $$f^{-1}(x) = 1$ for f(x) = 2$$ - \frac{1}{x}$$?

Accepted Answer

$$x = 1$$

Precalculus Test 1 Study Guide: Piecewise, Inverse, Logarithmic, Exponential, and Compound Interest Problems

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