Chapter 8

You buy a used truck for \(\$ 20,000\). It depreciates at the rate of \(15 \%\) per year. Find the value of the truck in the given years. 3 years

Find the balance after 5 years of an account that pays 4.8% interest compounded yearly given the following investment amounts. $$\$ 250$$

Use the quotient of powers property to simplify the expression. $$ \frac{x^{7} \cdot x}{x^{-2}} $$

Rewrite in scientific notation. $$ 0.0003 $$

Use the power of a power property to simplify the expression. $$ (-2)^{2} $$

You buy a used truck for \(\$ 20,000\). It depreciates at the rate of \(15 \%\) per year. Find the value of the truck in the given years. 8 years

Find the balance after 5 years of an account that pays 4.8% interest compounded yearly given the following investment amounts. $$\$ 300$$

Use the quotient of powers property to simplify the expression. $$ \left(\frac{1}{2}\right)^{5} $$

Rewrite in scientific notation. $$ 6,900,000 $$

Use the power of a power property to simplify the expression. $$ \left(2^{4}\right)^{3} $$

Rewrite as an expression with positive exponents. Tell whether the following statement is true. If a is positive, then \(a^{-n}\) is positive. Explain your reasoning.

You buy a used truck for \(\$ 20,000\). It depreciates at the rate of \(15 \%\) per year. Find the value of the truck in the given years. 10 years

Find the balance after 5 years of an account that pays 4.8% interest compounded yearly given the following investment amounts. $$\$ 350$$

Use the quotient of powers property to simplify the expression. $$ \left(\frac{3}{5}\right)^{3} $$

Rewrite in scientific notation. $$ 0.0000205 $$

Use the power of a power property to simplify the expression. $$ \left(4^{3}\right)^{3} $$

You buy a used truck for \(\$ 20,000\). It depreciates at the rate of \(15 \%\) per year. Find the value of the truck in the given years. 12 years

Find the balance after 5 years of an account that pays 4.8% interest compounded yearly given the following investment amounts. $$\$ 400$$

Use the quotient of powers property to simplify the expression. $$ \left(\frac{5}{m}\right)^{2} $$

Rewrite in scientific notation. $$ 72,000,000 $$

Use the power of a power property to simplify the expression. $$ \left(y^{4}\right)^{5} $$

Evaluate the exponential expression. Write fractions in simplest form. $$4^{-2}$$

A principal of \(\$ 200\) is deposited in an account that \(1-9\) pays \(4.2 \%\) interest compounded yearly. Find the balance after 5 years.

Use the quotient of powers property to simplify the expression. $$ \left(\frac{2}{b}\right)^{4} $$

Rewrite in scientific notation. $$ 0.000000006 $$

Use the power of a power property to simplify the expression. $$ \left(m^{4}\right)^{8} $$

Evaluate the exponential expression. Write fractions in simplest form. $$3^{-4}$$

INVESTING How much must you deposit in an account that pays \(3.5 \%\) interest compounded yearly to have a balance of \(\$ 400\) after 6 years?

Use the quotient of powers property to simplify the expression. $$ \left(\frac{5}{4}\right)^{-3} $$

Astronomy The distance between the ninth planet Pluto and the Sun is \(5.9 \times 10^{9}\) kilometers. Light travels at a speed of about \(3.0 \times 10^{5}\) kilometers per second. How long does it take light to travel from the Sun to Pluto?

Use the power of a product property to simplify the expression. $$ \left(2 m^{2}\right)^{3} $$

Evaluate the exponential expression. Write fractions in simplest form. $$\left(\frac{1}{5}\right)^{-1}$$

How much must you deposit in an account that pays \(6 \%\) interest compounded yearly to have a balance of \(\$ 1000\) after 8 years?

Use the quotient of powers property to simplify the expression. $$ \left(\frac{x^{4}}{2^{3}}\right)^{2} $$

DECIMAL FORM Rewrite in decimal form. $$ 2.14 \times 10^{4} $$

Use the power of a product property to simplify the expression. $$ \left(a b^{2}\right)^{2} $$

Evaluate the exponential expression. Write fractions in simplest form $$8\left(\frac{1}{4}\right)^{-1}$$

In the Chapter Opener you learned that there is a relationship between the breathing rate of a cyclist and the bicycle speed. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Bicycle speed, } x & 0 & 5 & 10 & 15 & 20 \\\\\hline \text { Breathing rate, } y & 6.4 & 10.7 & 18.1 & 30.5 & 51.4 \\\\\hline\end{array}$$ Let \(x\) represent the speed of the bike in miles per hour, and let \(y\) represent the cyclist's breathing rate in liters of air taken into the lungs per minute. The breathing rate of a cyclist can be modeled by \(y=6.37(1.11)^{x} .\) What is the cyclist's breathing rate if the bike is traveling 19 miles per hour? 25 miles per hour?

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=24(1.18)^{t}$$

Use the quotient of powers property to simplify the expression. $$ \left(\frac{x^{3}}{y^{5}}\right)^{6} $$

DECIMAL FORM Rewrite in decimal form. $$ 98 \times 10^{-2} $$

Use the power of a product property to simplify the expression. $$ (5 x)^{2} $$

Evaluate the exponential expression. Write fractions in simplest form $$4\left(4^{-2}\right)$$

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=14(0.98)^{t}$$

Use the quotient of powers property to simplify the expression. $$ \left(\frac{a^{6}}{b^{9}}\right)^{5} $$

DECIMAL FORM Rewrite in decimal form. $$ 7.75 \times 10^{0} $$

Use the power of a product property to simplify the expression. $$ \left(x^{3} y^{5}\right)^{4} $$

Evaluate the exponential expression. Write fractions in simplest form $$\left(\frac{1}{10}\right)^{-2}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{5^{6}}{5^{3}} $$

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=35\left(\frac{5}{4}\right)^{t}$$