91Ó°ÊÓ

Fill in the blanks. To ________ an equation in \( x \) means to find all values of \( x \) for which the equation is true.

In Exercises 5 - 12, determine whether each \( x \)-value is a solution (or an approximate solution) of the equation. \( 2^{3x + 1} = 32 \) (a) \( x = -1 \) (b) \( x = 2 \)

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places. Function \( f(x) = \left(\dfrac{2}{3}\right)^{5x} \) Value \( x = \dfrac{3}{10} \)

In Exercises 15 - 22, complete the table for a savings account in which interest is compounded continuously. Initial Investment \( \$1000 \) Annual % Rate \( 3.5\% \) Time to Double Amount After 10 Years

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. \( f(x) = \left(\dfrac{1}{2}\right)^x \)

In Exercises 15 - 22, evaluate the logarithm using the change-of-base formula. Round your result to three decimal \( \log_3 0.015 \)

In Exercises 29 - 44, find the exact value of the logarithmic expression without using a calculator. (If this is not possible,state the reason.) \( \log_6 \sqrt[3]{6} \)

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. \( f(x) = e^{-x} \)

The populations \( P \) (in thousands) of Horry County, South Carolina from \( 1970 \) through \( 2007 \) can be modeled by \( P = -18.5 + 92.2e^{0.0282t} \) where \( t \) represents the year, with \( t = 0 \) corresponding to 1970.(Source: U.S. Census Bureau) (a) Use the model to complete the table. (b) According to the model, when will the population of Horry County reach \( 300,000 \)? (c) Do you think the model is valid for long-term predictions of the population? Explain.

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is \( 250 \) bacteria, and the population after \( 10 \) hours is double the population after \( 1 \) hour. How many bacteria will there be after \( 6 \) hours?