Exam 4: Exponential and Logarithmic Functions

Approximate the number using a calculator. Round your answer to three decimal places. -A city is growing at the rate of $0.7 \%$ annually. If there were $3,767,000$ residents in the city in 1992, find how many (to the nearest ten-thousand) are living in that city in 2000 . Use $y = 3,767,000 ( 2.7 ) = .007 \mathrm { t }$ .

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 2 } { x } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 27 } { x } \right)$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = 3 - \log x$ .

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\left( \log _ { a } t - \log _ { a } s \right) + 4 \log _ { a } u$

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $2000 at 4% compounded annually for 14 years.

Choose the one alternative that best completes the statement or answers the question. Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 3.5 ( 0.9 ) ^ { x }$

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 0.9 } 14$

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 20 } 61.8$