Chapter 8

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

The function \(y=a b^{x}\) is a(n) \(\underline{?}\) function.

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

The expression \(\frac{a^{4}}{a^{6}}\) can be simplified by using the \(\underline{?}\) property.

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

In the expression \(a^{5}, a\) is called the_____of the expression.

Is \(y=1.02^{t}\) an exponential decay model? Explain.

Can \(\frac{x^{8}}{y^{3}}\) be simplified? Explain your answer.

Given the number \(6.39 \times 10^{7},\) would you move the decimal point to the left or to the right to rewrite the number in decimal form?

How are the expressions \(x^{7} \cdot x^{3}\) and \(\left(x^{7}\right)^{3}\) different? Explain your answer.

Evaluate the expression. \(3^{-1}\)

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

Rewrite in decimal form. $$ 4.3 \times 10^{2} $$

\(\operatorname{Can} a^{3} \cdot b^{4}\) be simplified? Explain your answer.

Evaluate the expression. \(0^{-4}\)

You deposit \(\$ 500\) in an account that pays \(4 \%\) interest compounded yearly. What is the balance after 5 years? after 10 years?

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 2 years

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

Rewrite in decimal form. $$ 8.11 \times 10^{3} $$

Use the product of powers property to simplify the expression. $$ c \cdot c \cdot c $$

Evaluate the expression. \(0^{0}\)

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 5 years

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

Rewrite in decimal form. $$ 8.11 \times 10^{3} $$

Use the product of powers property to simplify the expression. $$m \cdot m^{2}$$

Evaluate the expression. \(6 \cdot 3^{0}\)

You deposit \(\$1400\) in an account that pays 6% interest compounded yearly. Find the balance for the given time period. 5 years

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 8 years

Use the quotient of powers property to simplify the expression. $$ \frac{m^{5}}{m^{11}} $$

Rewrite in decimal form. $$ 9.38 \times 10^{5} $$

Use the product of powers property to simplify the expression. $$ 2^{2} \cdot 2^{3} $$

Rewrite as an expression with positive exponents. $$m^{-2}$$

You deposit \(\$1400\) in an account that pays 6% interest compounded yearly. Find the balance for the given time period. 8 years

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 10 years

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

Rewrite in decimal form. $$ 39.6 $$

Use the product of powers property to simplify the expression. $$ 3^{2} \cdot 3^{5} $$

Rewrite as an expression with positive exponents. $$3 c^{-5}$$

A business earned \(\$ 85,000\) in 1990 . Then its earnings decreased by \(2 \%\) each year for 10 years. Write an exponential decay model for the earnings \(E\) in year \(t\). Let \(t=0\) represent 1990 .

You deposit \(\$1400\) in an account that pays 6% interest compounded yearly. Find the balance for the given time period. 12 years

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

Rewrite in scientific notation. $$ 0.72 $$

Use the product of powers property to simplify the expression. $$ a^{4} \cdot a^{6} $$

Rewrite as an expression with positive exponents. $$a^{5} b^{-8}$$

You deposit \(\$1400\) in an account that pays 6% interest compounded yearly. Find the balance for the given time period. 20 years

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 simplify the expression. $$ x^{4} \cdot x^{5} $$

Rewrite in scientific notation. $$ 1200 $$

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

Rewrite as an expression with positive exponents. $$\frac{1}{(2 x)^{-3}}$$