Chapter 8

Graph the exponential decay model. $$ y=72(0.85)^{t} $$

An initial population of 1000 starfish doubles each year for 4 years. What is the starfish population after 4 years?

Simplify the quotient. $$ \frac{x^{3} \cdot x^{5}}{x^{2}} $$

Decide whether the number is in scientific notation. If not, write the number in scientific notation. $$ 0.7 \times 10^{2} $$

Write the expression as a single power of the base. \(\left(7^{4}\right)^{2}\)

Evaluate the expression without using a calculator. $$ \left(4^{-1}\right)^{-3} $$

Graph the exponential decay model. $$ y=10\left(\frac{1}{2}\right)^{t} $$

An ocean sunfish, the mola mola, is about 0.006 foot long when it hatches. By the time it reaches adulthood, the largest of the mola mola will have tripled its length about 7 times. What is the growth factor for the length of a mola mola?

Copy and complete the statement. $$ \left(\frac{1}{6}\right)^{4}=\frac{1}{?} $$

Decide whether the number is in scientific notation. If not, write the number in scientific notation. $$ 2.9 \times 10^{5} $$

Write the expression as a single power of the base. \(\left[(-4)^{5}\right]^{3}\)

Evaluate the expression without using a calculator. $$ \left(5^{-2}\right)^{2} $$

Graph the exponential decay model. $$ y=55\left(\frac{3}{4}\right)^{t} $$

Copy and complete the statement. $$ \left(\frac{-3}{5}\right)^{2}=\frac{?}{25} $$

An ocean sunfish, the mola mola, is about 0.006 foot long when it hatches. By the time it reaches adulthood, the largest of the mola mola will have tripled its length about 7 times. What is the maximum length of an adult mola mola?

Decide whether the number is in scientific notation. If not, write the number in scientific notation. $$ 10 \times 10^{-3} $$

Graph the exponential function. $$y=4^{x}$$

Write the expression as a single power of the base. \(\left(t^{5}\right)^{6}\)

Evaluate the expression without using a calculator. $$ \left(3^{2}\right)^{-1} $$

Write an exponential decay model for the situation. Then graph the model and use the graph to estimate the value at the end of the given time period. A 22,000 dollar investment decreases in value by \(9 \%\) per year for 8 years.

Use the following information. The air intake b (in liters per minute) of a cyclist on a racing bike can be modeled by \(b=6.37(1.11)^{s},\) where s is the speed of the bike (in miles per hour). Use a calculator to find the cyclist’s air intake if the racing bike is traveling 7 miles per hour, 19 miles per hour, or 25 miles per hour.

Copy and complete the statement. $$ \left(\frac{2}{7}\right)^{?}=\frac{8}{343} $$

Write the number in scientific notation. $$ 900 $$

Graph the exponential function. $$y=-7^{x}$$

Write the expression as a single power of the base. \(\left(c^{8}\right)^{10}\)

Evaluate the expression without using a calculator. $$ \left[(-8)^{-2}\right]^{-1} $$

Write an exponential decay model for the situation. Then graph the model and use the graph to estimate the value at the end of the given time period. A population of 2,000,000 decreases by 2% per year for 15 years.

Copy and complete the statement. $$ \left(\frac{x}{y}\right)^{?}=\frac{y^{2}}{x^{2}} $$

Use the following information. The air intake b (in liters per minute) of a cyclist on a racing bike can be modeled by \(b=6.37(1.11)^{s},\) where s is the speed of the bike (in miles per hour). Graph the exponential growth model.

Write the number in scientific notation. the number $$ 700,000,000 $$

Graph the exponential function. $$y=4(2)^{x}$$

Write the expression as a single power of the base. \(\left(x^{3}\right)^{2}\)

Evaluate the expression without using a calculator. $$ (10 \cdot 2)^{-2} $$

You buy a new motorcycle for $10,500. It’s value depreciates by 10% each year for the 10 years you own it.

Copy and complete the statement. $$ \left(\frac{a^{2}}{b}\right)^{5}=\frac{a^{?}}{b^{5}} $$

Write the number in scientific notation. the number $$ 88,000,000 $$

Graph the exponential function. $$y=-3(8)^{x}$$

Simplify the expression. \((3 \cdot 7)^{2}\)

Evaluate the expression without using a calculator. $$ (1 \cdot 7)^{-3} $$

In Exercises 38–41, use the following information. From 1894 to 1903 the number of miles of cable car track in the United States decreased by about 11% per year. There were 302 miles of track in 1894. Write an exponential decay model showing the number of miles of cable car track left each year.

Copy and complete the statement. $$ \left(\frac{m^{3}}{n^{?}}\right)^{4}=\frac{m^{12}}{n^{8}} $$

Write the number in scientific notation. the number $$ 1012 $$

Graph the exponential function. $$y=\left(\frac{1}{2}\right)^{x}$$

Simplify the expression. \((4 \cdot 9)^{3}\)

Evaluate the expression without using a calculator. $$ (-2 \cdot 2)^{-2} $$

Simplify the quotient. $$ \left(\frac{1}{5}\right)^{4} $$

Write the number in scientific notation. the number $$ 95.2 $$

Graph the exponential function. $$y=\left(\frac{2}{5}\right)^{x}$$

Simplify the expression. \((-4 \cdot 6)^{2}\)

Evaluate the expression without using a calculator. $$ [4 \cdot(-3)]^{-1} $$