Stewart Precalc 6e Chapter 4 Test: Exponential and Logarithmic Functions

1 Test - Graphing exponential and logarithmic functions · Level 2

Sketch the graph of each function, and state its domain, range, and asymptote. Show the $x$- and $y$-intercepts on the graph.

(a) $f(x) = 2^{-x} + 4$

Answer for 1(a)

(b) $g(x) = \log_3(x + 3)$

Answer for 1(b)

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2 Test - Converting between exponential and logarithmic forms · Level 2

(a) Write the equation in logarithmic form. $6^{2x} = 25$

Answer for 2(a)

(b) Write the equation $\ln A = 3$ in exponential form.

Answer for 2(b)

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3 Test - Evaluating logarithmic expressions · Level 2

Find the exact value of each expression.

(a) $10^{\log 36}$

Answer for 3(a)

(b) $\ln e^3$

Answer for 3(b)

(c) $\log_3 \sqrt{27}$

Answer for 3(c)

(d) $\log_2 80 - \log_2 10$

Answer for 3(d)

(e) $\log_8 4$

Answer for 3(e)

(f) $\log_6 4 + \log_6 9$

Answer for 3(f)

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4 Test - Expanding logarithms · Level 2

Use the Laws of Logarithms to expand the expression: $ \log \sqrt[3]{\dfrac{x + 2}{x^4 (x^2 + 4)}} $

5 Test - Combining logarithms · Level 2

Combine into a single logarithm: $ \ln x - 2 \ln(x^2 + 1) + \dfrac{1}{2} \ln(3 - x^4) $

6 Test - Solving exponential and logarithmic equations · Level 3

Find the solution of the equation, correct to two decimal places.

(a) $2^{x - 1} = 10$

Answer for 6(a)

(b) $5 \ln(3 - x) = 4$

Answer for 6(b)

(c) $10^{x + 3} = 6^{2x}$

Answer for 6(c)

(d) $\log_2(x + 2) + \log_2(x - 1) = 2$

Answer for 6(d)

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7 Test - Bacterial growth modeling · Level 3

The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 8000.

(a) Find a function that models the population after $t$ hours.

Answer for 7(a)

(b) Find the population after 1.5 hours.

Answer for 7(b)

(c) When will the population reach 15,000?

Answer for 7(c)

(d) Sketch the graph of the population function.

Answer for 7(d)

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8 Test - Compound interest · Level 3

Suppose that \$12,000 is invested in a savings account paying 5.6\% interest per year.

(a) Write the formula for the amount in the account after $t$ years if interest is compounded monthly.

Answer for 8(a)

(b) Find the amount in the account after 3 years if interest is compounded daily.

Answer for 8(b)

(c) How long will it take for the amount in the account to grow to \$20,000 if interest is compounded semiannually?

Answer for 8(c)

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9 Test - Radioactive decay · Level 3

The half-life of krypton-91 (Kr-91) is 10 seconds. At time $t = 0$ a heavy canister contains 3 g of this radioactive gas.

(a) Find a function that models the amount $A(t)$ of Kr-91 remaining in the canister after $t$ seconds.

Answer for 9(a)

(b) How much Kr-91 remains after one minute?

Answer for 9(b)

(c) When will the amount of Kr-91 remaining be reduced to 1 $\mu$g (1 microgram, or $10^{-6}$ g)?

Answer for 9(c)

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10 Test - Richter scale · Level 3

An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007, causing extensive damage. Earlier that year, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania. How many times more intense was the Japanese earthquake than the Pennsylvania earthquake?

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