Exponential Functions & Logarithms

Exponential Functions and the Natural Base e

100

What is the approximate value of e?

~2.718

Bonus: What is an alternative name for e (other than "the natural base)?

200

Tell whether the function is exponential growth or decay: y = (4.25)^x

Explain your reasoning.

Exponential growth; the base is greater than 1

300

The value of a car can be approximated by the model y = 25(0.9)^t. Identify the percent decrease in the value of the car.

10%

400

Simplify the expression: (5e^4x)³

125e^12x

500

You deposit $250 in an account that pays 1.25% annual interest. Find the balance after 3 years when the interest is compounded quarterly.

A = $259.54

Logarithms and Logarithmic Functions

100

Fill in the blanks:

A common logarithm is a logarithm with base ___. A _____ logarithm is a logarithm with base e.

10; natural

200

Rewrite the exponential equation in logarithmic form:

16^3/4 = 8

log₁₆8 = 3/4

300

Evaluate log₈(1/512) without a calculator

-3

400

Find the inverse of y = ln(x-5)

y = e^x + 5

500

What is the domain and range of the graph of a logarithmic function?

Domain: non-negative values for x

Range: All real numbers

Bonus: Sketch the graph of a logarithmic function whose base is between 0 and 1

Properties of Logs

100

State the names of the three logarithmic properties

Product, Quotient, and Power

200

True or false:

log₆13 = log 13/log 6 = ln 13/ ln 6

True

300

Use the change of base formula to evaluate log₂19

4.248

400

Condense log 6 + 4 log 3 - log 3

log 162

500

Expand ln (5/12x)

ln 5 - ln 12 - ln x

Solving Exponential and Logarithmic Equations

100

Solve ln(5x + 2) = ln(x + 10)

x = 2

200

Solve 81^x = (1/9)^{x + 3}​​​​

x = -1

300

Solve 2^x < 36

x < 5.170

400

Solve log₆6x + log₆(x - 1) = 2

x = 3

500

You cook a turkey until the internal temperature reaches 180^oF. The turkey is placed on the table until the internal temperature reaches 100^oF and it can be carved. When the room temperature is 72^oF, the cooling rate of the turkey is r = 0.067. How long do you have to wait until you can carve the turkey?

about 20 minutes

Random

100

Solve 3^x = 8

x = 1.893

200

Rewrite the logarithmic equation in exponential form: log₃81 = 4

3⁴ = 81

300

Tell whether the function represents exponential growth or decay: y = 0.5e^x

Explain your reasoning.

Exponential growth; a > 0 and r > 0

400

One hundred grams of radium are stored in a container. The amount R (in grams) of radium present after t years can be modeled by R = 100e^-0.00043t. After how many years will only 5 grams of radium be present?

About 6967 years

500

You deposit $100 in an account that pays 6% annual interest. If the interest is compounded continuously, how long will it take for the balance to reach $1000?

38.38 years