Exponentials/Logarithms

Exponential Functions

100

Is the function exponential growth or decay?

4(1/3)^x

What is decay?

200

What is the initial value of the exponential function?

f(x)= 4(1.5)^x

What is 4?

300

What is the percent the exponential function is growing by?

g(x)=300(1.10)^x

What is 10 percent?

400

What is the percent the exponential is decaying by?

k(x) = 75(0.85)^x

What is 15 percent?

500

An exponential function crosses through the two points (-1, 4) and (0,2). Write the equation for the function.

What is f(x) = 2(1/2)^x

Exponential Word Problems

100

Every hour, the amount of people in line for a concert doubles. What is the growth factor for the exponential function?

What is 2?

200

What is the equation for compound continuous growth?

What is A = Pe^rt

300

Dolphin populations are declining at an alarming rate. Currently there are only 300,000 left in the ocean, if every year they lose 15% of the population, how many dolphins will be left after 2 years?

What is 216,750?

400

Write the exponential equation for the following situation: The amount of bacteria on a moldy piece of bread is multiplied by 1.5 times every hour. At the start of the day, there was 10 bacteria.

What is 10(1.5)^x?

500

Debbie invests $1000 into an account compounded semiannually with a 5% interest rate. How much money does she have after 3 years?

What is $1159.69?

Simple Logarithms

100

What is the value of log₂2?

What is 1?

200

What is the value of ln(e³)?

What is 3?

300

Rewrite the logarithmic equation as an exponential equation: log₅125 = 3

What is 5³ = 125?

400

Solve the logarithm for x: log₃ 27 = x

What is 3?

500

Solve the logarithm for x: log_x 8 = 3

What is 2?

Logarithm Properties

100

Rewrite the logarithm without an exponent: 

log5⁶

What is 6log5?

200

Solve for x:

log2x = log 8

What is x = 4?

300

Expand the logarithm:

log₃(18/7) = 

What is log₃ 18 - log₃7?

400

Condense the logarithm:

log₆x + log₆ 3

What is log₆3x?

500

Solve for x:

ln(4x-6)=ln(54-2x)

What is x = 10?

Solving Logs/Exponentials

100

Solve the exponential for x: 2^x = 8

What is x = 3?

200

Solve for x:

e^x/4 = 7

What is x = 4ln7?

or 7.78?

300

Solve for x:

3^x = 78

What is x = log₃78?

or 3.97?

400

Solve for x:

75 (10^2x ) = 300

What is x = (log4)/2?

or 0.30?

500

Andre deposits $300 into a bank account compounded continuously with a 4% interest rate. How long will it take him to double his money?

What is 17.33 years?