Chapter 8

Write the number in decimal form. $$ 7.75 \times 10^{0} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=9^{x}$$

Write the expression as a single power of the base. \(t^{3} \cdot t^{2}\)

Evaluate the expression. $$ (-7)^{-3} $$

You buy a used truck for 20,000 dollar. The truck depreciates 7% per year. Find the value of the truck after the given number of years. $$12 years$$

You deposit \(\$900\) in an account that compounds interest yearly. Find the balance after 10 years for the given interest rate. $$5 \%$$

Simplify the quotient. $$ \frac{5^{6}}{5^{3}} $$

Write the number in decimal form. $$ 4.33 \times 10^{8} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=8(2)^{x}$$

Copy and complete the statement. \(\left(5^{?}\right)^{3}=5^{9}\)

Evaluate the expression. $$ \frac{1}{10^{-1}} $$

In Exercises 26–28, use the following information. The amount of aspirin y (in milligrams) in a person’s blood can be modeled by y A(0.8)t where A represents the dose of aspirin taken (in milligrams) and t represents the number of hours since the aspirin was taken. Find the amount of aspirin remaining in a person’s blood for the given dosage and time. $$Dosage: 250 \mathrm{mg}\quad Time: after 2 hours$$

You deposit \(\$900\) in an account that compounds interest yearly. Find the balance after 10 years for the given interest rate. $$6 \%$$

Simplify the quotient. $$ \frac{8^{2}}{8^{3}} $$

Write the number in decimal form. $$ 3 \times 10^{-4} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=3(4)^{x}$$

Evaluate the expression. $$ \frac{1}{4^{-4}} $$

Use the following information. The amount of aspirin y (in milligrams) in a person’s blood can be modeled by y A(0.8)t where A represents the dose of aspirin taken (in milligrams) and t represents the number of hours since the aspirin was taken. Find the amount of aspirin remaining in a person’s blood for the given dosage and time. $$Dosage: 500 \mathrm{mg} \quad Time: after 3.5 hours$$

You deposit \(\$900\) in an account that compounds interest yearly. Find the balance after 10 years for the given interest rate. $$7 \%$$

Simplify the quotient. $$ \frac{(-3)^{6}}{(-3)^{6}} $$

Write the number in decimal form. $$ 9 \times 10^{-3} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=\left(\frac{1}{9}\right)^{x}$$

Copy and complete the statement. \(\left[(-9)^{4}\right]^{3}=(-9)^{?}\)

Evaluate the expression. $$ \frac{1}{(-8)^{-2}} $$

Use the following information. The amount of aspirin y (in milligrams) in a person’s blood can be modeled by y A(0.8)t where A represents the dose of aspirin taken (in milligrams) and t represents the number of hours since the aspirin was taken. Find the amount of aspirin remaining in a person’s blood for the given dosage and time. $$Dosage: 750 \mathrm{mg} \quad Time: after 5 hours$$

Identify the growth rate and the growth factor in the exponential function. $$y=50(1+1)^{t}$$

Simplify the quotient. $$ \frac{6^{3} \cdot 6^{2}}{6^{5}} $$

Write the number in decimal form. $$ 4 \times 10^{-5} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=\left(\frac{5}{8}\right)^{x}$$

Copy and complete the statement. \(\left(a^{2}\right)^{?}=a^{10}\)

In Exercises 29 and 30, use the following information. At the start of a basketball tournament consisting of six rounds, there are 64 teams. After each round, one half of the remaining teams are eliminated. Write an exponential decay model showing the number of teams left in the tournament after each round.

Identify the growth rate and the growth factor in the exponential function. $$y=31(4)^{t}$$

Simplify the quotient. $$ \frac{x^{4}}{x^{5}} $$

Write the number in decimal form. $$ 9.8 \times 10^{-2} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=6\left(\frac{1}{2}\right)^{x}$$

Copy and complete the statement. \(\left(x^{3}\right)^{3}=x^{?}\)

Evaluate the expression without using a calculator. $$ 10^{-5} \cdot 10^{7} $$

Use the following information. At the start of a basketball tournament consisting of six rounds, there are 64 teams. After each round, one half of the remaining teams are eliminated. How many teams remain after 3 rounds? after 4 rounds?

Identify the growth rate and the growth factor in the exponential function. $$y=5.6(2.3)^{t}$$

Simplify the quotient. $$ x^{3} \cdot \frac{1}{x^{2}} $$

Write the number in decimal form. $$ 6.02 \times 10^{-6} $$

Use a calculator to evaluate the exponential function when \(x=2.5 .\) Round your answer to the nearest hundredth. $$y=-\left(\frac{3}{5}\right)^{x}$$

Copy and complete the statement. \(\left(p^{2}\right)^{6}=p^{12}\)

Evaluate the expression without using a calculator. $$ 6^{2} \cdot 6^{-4} $$

Graph the exponential decay model. $$ y=15(0.9)^{t} $$

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

Simplify the quotient. $$ \frac{1}{x^{8}} \cdot x^{5} $$

Write the number in decimal form. $$ 1.1 \times 10^{-10} $$

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

Evaluate the expression without using a calculator. $$ 4^{-1} \cdot 4^{-1} $$