Chapter 8

Tell whether the statement is true or false. Explain your answer. A nonzero number to the zero power is zero.

In the exponential decay model, y=C(1-r)^{t}, what is the decay factor?

Complete: In the exponential growth model,\(y=C(1+r)^{t}\),C is the___? and \((1+r)\) is the ____?

Is the number \(12.38 \times 10^{2}\) in scientific notation? Explain.

Match the division property of exponents with the example that illustrates it. A. \(\left(\frac{3}{6}\right)^{2}=\frac{3^{2}}{6^{2}}\) B. \(\frac{4^{3}}{4^{5}}=4^{3-5}\) Quotient of powers property

Define exponential function.

Tell whether the statement is true or false. Explain your answer. Let \(a\) be a nonzero number and let \(n\) be an integer. Then \(a^{-n}=\frac{1}{a^{n}}\)

A business earned $85,000 in 1990. Then its earnings decreased by 2% each year for 10 years. Write an exponential decay model to represent the decreasing annual earnings of the business.

You deposit $500 in an account that pays 4% interest compounded yearly. What is the initial amount P?

Write the number in decimal form. $$ 9 \times 10^{4} $$

Match the division property of exponents with the example that illustrates it. A. \(\left(\frac{3}{6}\right)^{2}=\frac{3^{2}}{6^{2}}\) B. \(\frac{4^{3}}{4^{5}}=4^{3-5}\) Power of a quotient property

Copy and complete the table of values for the exponential function. $$\begin{array}{|c|c|c|c|c|c|c|}\hline x & {-2} & {-1} & {0} & {1} & {2} & {3} \\\ \hline y=4^{x} & {?} & {?} & {?} & {?} & {?} & {?} \\ \hline\end{array}$$

Evaluate the expression. $$ 6^{0} $$

You buy a used car for 7000 dollar. The car depreciates at the rate of 6% per year. Find the value of the car after the given number of years. $$2 years$$

Write the number in decimal form. $$ 4.3 \times 10^{2} $$

Use the quotient of powers property to simplify the expression. $$ \frac{5^{4}}{5^{1}} $$

Match the multiplication property of exponents with the example that illustrates it. Power of a product property A. \((3 \cdot 6)^{2}=3^{2} \cdot 6^{2}\) B. \(4^{3} \cdot 4^{5}=4^{3+5}\) C. \(\left(2^{4}\right)^{4}=2^{4} \cdot 4\)

Evaluate the expression. $$ 3^{-1} $$

You buy a used car for 7000 dollar. The car depreciates at the rate of 6% per year. Find the value of the car after the given number of years. $$5 years$$

You deposit \(\$500\) in an account that pays 4% interest compounded yearly. Complete this equation to write an exponential growth model for the balance after t years: \(A=?(1+?)^{t}\)

Write the number in decimal form. $$ 8.11 \times 10^{3} $$

Use the quotient of powers property to simplify the expression. $$ \frac{7^{6}}{7^{9}} $$

Graph the function \(y=3\left(\frac{1}{4}\right)^{x}\)

Use the product of powers property to write the expression as a single power of the base. \(2^{2} \cdot 2^{3}\)

Evaluate the expression. $$ \frac{1}{4^{-3}} $$

You buy a used car for 7000 dollar. The car depreciates at the rate of 6% per year. Find the value of the car after the given number of years. $$8 years$$

Write the number in decimal form. $$ 5 \times 10^{-2} $$

Use the quotient of powers property to simplify the expression. $$ \frac{(-2)^{8}}{(-2)^{3}} $$

Use the product of powers property to write the expression as a single power of the base. \((-5)^{4} \cdot(-5)^{2}\)

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

You buy a used car for 7000 dollar. The car depreciates at the rate of 6% per year. Find the value of the car after the given number of years. $$10 years$$

Write the number in decimal form. $$ 9.4 \times 10^{-5} $$

Use the quotient of powers property to simplify the expression. $$ \frac{5^{3} \cdot 5^{5}}{5^{9}} $$

Use the product of powers property to write the expression as a single power of the base. \(a^{4} \cdot a^{6}\)

Evaluate the expression without using a calculator. $$ 2^{-4} \cdot 2^{5} $$

Identify the initial amount and the growth rate in the exponential function. $$y=100(1+0.5)^{t}$$

Write the number in decimal form. $$ 2.45 \times 10^{-1} $$

Use the quotient of powers property to simplify the expression. $$ \frac{x^{12}}{x^{9}} $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=2^{x}$$

Use the power of a power property to write the expression as a single power of the base. \(\left(2^{4}\right)^{3}\)

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

Classify the model as exponential growth or exponential decay. $$ y=0.55(3)^{t} $$

Identify the initial amount and the growth rate in the exponential function. $$y=12(1+2)^{t}$$

Write the number in scientific notation. $$ 15 $$

Use the quotient of powers property to simplify the expression. $$ \frac{a^{5}}{a^{2}} $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=5^{x}$$

Use the power of a power property to write the expression as a single power of the base. \(\left(4^{3}\right)^{3}\)

Evaluate the expression without using a calculator. $$ (4 \cdot 1)^{-2} $$

Classify the model as exponential growth or exponential decay. $$ y=3(0.55)^{t} $$

Identify the initial amount and the growth rate in the exponential function. $$y=7.5(1.75)^{t}$$