Free Printable MAT 171 Sections 3.1-3.3

1.

Use the compound interest formulas A = $P(1+r/n)^{nt}$ and $A=Pe^{rt}$ to solve. Find the accumulated value of an investment of $18,000 at 8% compounded annually for 14 years.

a)

$52,869.49

b)

$38,160.00

c)

$36,720.00

d)

$48,953.23

2.

Write the equation in its equivalent exponential form. $\log_3 x = 2$

a)

$x^2=3$

b)

3x = 2

c)

$2^3=x$

d)

$3^2=x$

3.

Write the equation in its equivalent logarithmic form. $\sqrt[3]{8}=2$

a)

$\log_8 3 = \frac{1}{2}$

b)

$\log_2 8 = 3$

c)

$\log_8 2 = \frac{1}{3}$

d)

$\log_2 8 = \frac{1}{3}$

4.

Find the domain of the logarithmic function. $f(x) = \ln (4 - x)$

a)

(-4, ∞)

b)

(-∞, 0)

c)

(-∞, 4) or (4, ∞)

d)

(-∞, 4)

5.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\log_5 (125x)$

a)

15 + $\log_5 x$

b)

3x

c)

3 + $\log_5 x$

d)

3 $\log_5 x$

6.

Expand: $\log_{12}\left(\frac{12}{x}\right)$

a)

$-\log_{12}x$

b)

$1-\log_{12}x$

c)

$\frac{1}{x}$

d)

12

7.

$\log_2\left(\frac{x^4}{y^6}\right)$

a)

$4\log_2x+6\log_2y$

b)

$\frac{2}{3}\log_2\left(\frac{x}{y}\right)$

c)

$6\log_2y-4\log_2x$

d)

$4\log_2x-6\log_2y$

8.

Use properties of logarithms to condense the logarithmic expression. Write the expression as logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. $5\log_bt-\log_bs$

a)

$\log_b(t^5-s)$

b)

$\log_b\left(\frac{5t}{s}\right)$

c)

$\log_b\left(\frac{t^5}{s}\right)$

d)

$\log_bt^5+\log_bs$

9.

A train ticket in a certain city is $2.00. People who use the train also have the option of purchasing a frequent rider pass for 18.75 each month. With the pass, each ticket costs only $1.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the monthly cost with the pass.

a)

27 times

b)

24 times

c)

25 times

d)

26 times

10.

You inherit $10,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 11% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $700?

a)

$8000 invested at 6% $2000 invested at 11%

b)

$7000 invested at 6%

$3000 invested at 11%

c)

$9000 invested at 6% $1000 invested at 11%

d)

$2000 invested at 6%

$8000 invested at 11%

MAT 171 Sections 3.1-3.3

Total questions: 10

Worksheet time: 57mins

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