91Ó°ÊÓ

Write each expression as a single natural logarithm. \(2 \ln 8-3 \ln 4\)

State the property or properties used to rewrite each expression. \(2 \log w+4 \log z=\log w^{2} z^{4}\)

Population The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26\(\% .\) a. Find the growth factor for the world population. b. Suppose the rate of increase continues to be 1.26\(\% .\) Write a function to model world population growth.

Botany Phosphorus- 32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write the exponential decay function for a 50 -mg sample. Find the amount of phosporus- 32 remaining after 84 days.

Archaeology Carbon-14 is used to determine the age of artifacts in carbon dating. It has a half-life of 5730 years. Write the exponential decay function for a \(24-\mathrm{mg}\) sample. Find the amount of carbon- 14 remaining after 30 millennia \((1 \text { millennium }=1000 \text { years). }\)

Find the amount in a continuously compounded account for the given conditions. principal: \(\$ 950\) annual interest 6.5\(\%\) time: 10 yr

The pH of each food is given. Find the concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right] .\) lime juice, 2.2

Use the Change of Base Formula to evaluate each expression. Then convert it to a logarithm in base \(8 .\) $$ \log _{2} 7 $$

For each function, find the percent increase or decrease that the function models. $$ y=0.65(1.3)^{x} $$

Gridded Response The battery power available to run a satellite is given by the formula \(P=50 e^{-\frac{t}{250}}\) , where \(P\) is power in watts and \(t\) is time in days. For how many days can the satellite run if it requires 15 watts?