Q: Paula invests $$\1$$,300$$ compounded continuously at 6$$\%$$ for 13$ years. What is the amount she will have? (Use A$$ = $$Pe^{rt}$)

$$A = 1300 e$$^{0.06 \times 13}$$

Question 1

Given the function $$f(x) = 2^x + 3$$, which of the following is the correct domain of $$f(x)$$?

Accepted Answer

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

Question 2

Given $$f(x) = 2^x + 3$$, what is the horizontal asymptote of the graph of $$f(x)$$?

Accepted Answer

$$y = 3$$

Question 3

Write $$32 = 8^x in $$logarithmic form.

Accepted Answer

$$x = \log_8$ 32$$

Question 4

Express $$\log_3$ a = b in $$exponential form.

Accepted Answer

$$a = 3^b$$

Question 5

Simplify $$4\log x - 3\log y + \log z as a $$single logarithm.

Accepted Answer

$$\log \left( \dfrac{x^4$ z}{y^3$} \right)$$

Question 6

Rewrite $$\log_2$ \left( \dfrac{5x^3$ y}{z} \right) as $$the sum and/or difference of logarithms.

Accepted Answer

$$\log_2$ 5 + 3\log_2$ x + \log_2$ y - \log_2$ z$$

Question 7

What is the vertical asymptote of the function $$f(x) = \log(x + 7)$$?

Accepted Answer

$$x = -7$$

Question 8

Use the change of base formula to find $$\log_6$ 5. $$Which of the following is correct?

Accepted Answer

$$\dfrac{\log 5}{\log 6}$$

Question 9

Solve for $$x$$: $$5 + 3e^x = 68$$

Accepted Answer

$$x = \ln 21$$

Question 10

If $$f(x) = 4x - 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 7}{4}$$

Question 11

A $$\4$$,500$$ investment is compounded monthly at 5$$\%$$ for 6$ years. What is the amount at the end of 6$ years? (Use A = P$$\left(1 + \dfrac{r}{n}\$$right)^{nt}$)

Accepted Answer

$$A = 4500\left(1 + \dfrac{0.05}{12}\$$right)^{72}$$

Question 12

Paula invests $$\1$$,300$$ compounded continuously at 6$$\%$$ for 13$ years. What is the amount she will have? (Use A$$ = $$Pe^{rt}$)

Accepted Answer

$$A = 1300 e$$^{0.06 	imes 13}$$

Question 13

Given the exponential model $$P(t) = 45.2e$$^{0.018t}$$ for a city's population in thousands, what was the initial population in 2010?

Accepted Answer

$$45,200$$

Question 14

Which of the following exponential models represents a decreasing population?

Accepted Answer

$$A = 12.8e$$^{-0.009t}$$

Question 15

The logistic growth model for a fish population is $$P(t) = \dfrac{80}{1 + 15e$$^{-0.15t}$$}. $$What is the limiting size of the fish population?

Accepted Answer

$$80$$ thousand

Question 16

Which transformation describes the change from $$f(x) = 5^x to$$ $$f(x) = 5$$^{-x}$$?

Accepted Answer

Reflection across the $$y-$$axis

Question 17

If $$f$$ and $$g$$ are inverse functions, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Question 18

Given $$f(x) = \ln x$$, which transformation results in $$f(x) = 2 + \ln(x + 1)$$?

Accepted Answer

Shift left by 1 unit and up by 2 units

Question 19

The graph of $$g(x) = \log_b(x + 3)$$ approaches, but does not touch, which axis? What is the equation of this axis?

Accepted Answer

The $$y-$$axis; $$x = -3$$

College Algebra Test 3 Review – Step-by-Step Guidance

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