10.2 Evaluate and Graph Exponential Functions

Before you get started, take this readiness quiz.

Simplify: $\left(\frac{x^{3}}{x^{2}}\right) .$
If you missed this problem, review the reference.

Evaluate: ⓐ $2^{0}$ ⓑ $\left(\frac{1}{3}\right)^{0} .$
If you missed this problem, review the reference.

Evaluate: ⓐ $2^{−1}$ ⓑ $\left(\frac{1}{3}\right)^{−1} .$
If you missed this problem, review the reference.

Solve: $3^{3 x - 2} = 81 .$

Solve: $7^{x - 3} = 7 .$

Solve: $\frac{e^{x^{2}}}{e^{x}} = e^{2} .$

Solve: $\frac{e^{x^{2}}}{e^{x}} = e^{6} .$

A total of $\$ 10,000$ was invested in a college fund for a new grandchild. If the interest rate is $5 \% ,$ how much will be in the account in 18 years by each method of compounding?

ⓐ compound quarterly

ⓑ compound monthly

ⓒ compound continuously

Angela invested $\$ 15,000$ in a savings account. If the interest rate is $4 \% ,$ how much will be in the account in 10 years by each method of compounding?

ⓐ compound quarterly

ⓑ compound monthly

ⓒ compound continuously

Allan invested $10,000 in a mutual fund. If the interest rate is $5 \% ,$ how much will be in the account in 15 years by each method of compounding?

ⓐ compound quarterly

ⓑ compound monthly

ⓒ compound continuously

Chris is a researcher at the Center for Disease Control and Prevention and he is trying to understand the behavior of a new and dangerous virus. He starts his experiment with 100 of the virus that grows continously at a rate of 25% per hour. He will check on the virus in 24 hours. How many viruses will he find?

Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts her experiment with 50 of the bacteria that grows at a rate of $15 \%$ per hour. She will check on the bacteria every 8 hours. How many bacteria will she find in 8 hours?

Milan, a biologist is observing the growth pattern of a virus. They start with 100 of the virus that grows at a rate of $10 \%$ per hour. They will check on the virus in 24 hours. How many viruses will they find?

Solve each equation.

$2^{3 x - 8} = 16$

Solve each equation.

$3^{x + 3} = 9$

Solve each equation.

$4^{x^{2}} = 4$

Solve each equation.

$4^{x + 2} = 64$

Solve each equation.

$2^{x^{2} + 2 x} = \frac{1}{2}$

Solve each equation.

$e^{3 x} \cdot e^{4} = e^{10}$

Solve each equation.

$\frac{e^{x^{2}}}{e^{2}} = e^{x}$

Use an exponential model to solve.

Edgar accumulated $\$ 5,000$ in credit card debt. If the interest rate is $20 \%$ per year, and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by each method of compounding? ⓐ compound quarterly ⓑ compound monthly ⓒ compound continuously

Use an exponential model to solve.

Rochelle deposits $\$ 5,000$ in an IRA. What will be the value of her investment in 25 years if the investment is earning $8 \%$ per year and is compounded continuously?

Use an exponential model to solve.

A researcher at the Center for Disease Control and Prevention is studying the growth of a bacteria. He starts his experiment with 100 of the bacteria that grows at a rate of $6 \%$ per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours?

Use an exponential model to solve.

In the last ten years the population of Indonesia has grown at a rate of $1.12 \%$ per year to 258,316,051. If this rate continues, what will be the population in 10 more years?

Explain how you can distinguish between exponential functions and polynomial functions.

What happens to an exponential function as the values of $x$ decreases? Will the graph ever cross the
$x$-axis? Explain.