Exponential and Logarithmic Functions

Exponential Function

100

Determine whether the equation represents exponential growth, exponential decay, or neither, 
y=220(1.06)x

What is Exponential Growth?

200

Determine whether the equation represents exponential growth, exponential decay, or neither,
y=11,701(0.97)t

What is Exponential Decay?

300

Determine whether the equation represents continuous growth, continuous decay, or neither, y=3742(e)^.75t

What is continuous growth?

400

Determine whether the equation represents continuous growth, continuous decay, or neither, y=2.25(e)^-2t

What is continuous decay?

500

Evaluate the function f(x)= -4^2x+3, when F(-1)

What is -4?

Logarithmic Function

100

Rewrite the equation log_y(x)=−11 into exponential form

What is y^-11=x?

200

Rewrite c^d= k into logarithmic form

What is log_c(k)= d?

300

Solve for x in the equation log(x)=3

What is x=1000?

400

Solve for x in the equation log₉(x)=1/2

What is x=3?

500

Evaluate the base b logarithmic equation when the function is 6log₈(4)

What is 4?

Logarithmic Properties

100

Expand this logarithm, log_b(7x⋅2y)

What is log_b(2)+log_b(7)+log_b(x)+log_b(y)?

200

Condense the equation into a single logarithm, log_b(28)−log_b(7)

What is log_b(4)?

300

Expand the logarithm as much as possible, log(x¹⁵y¹³/z¹⁹)

What is 15log(x) + 13log(y) - 19log(z)?

400

Condense the expression to a single logarithm,    log(x)−1/2log(y)+3log(z)

What is log(xz^3/√y)?

500

Evaluate the following expression without using a calculator, 6log₈(2)+log₈(64)/3log₈(4)

What is 3?

Exponential and Logarithmic Equations

100

Use like bases to solve the exponential equation, 64⋅4^3x=16

What is x=-1/3?

200

Use logarithms to solve,
e^r+10−10=−42

What is No Solution?

300

Use logarithms to solve, −8⋅10^p+7−7=−24

What is p= log(17/8) - 7?

400

Use logarithms to solve,
−6e^9x+8+2=−74

What is x= ln(38/3)-8/9?

500

Use definition of logarithm to solve the equation,
4+log₂(9k)=2

What is k= 1/36?

Exponential and Logarithmic Models

100

Use the logistic growth model f(x)= 150/1+8e^-2x, to find f(0)

What is f(0)= 16.7?

200

Find the carrying capacity in f(x)=150/1+8e^-2x

What is 150?

300

Find the doubling time for fish population using the function P(t)= 1000/1+9e^-.6t

What is 1.4 years?

400

Find how long it will take for the population to reach 900 fish using P(t)= 1000/1+9e^-.6t

What is 7.3 years?

500

Use the equation N(t)= 500/1+.49e^-.7t, where t represents days and N represents people, find how many people will have heard the rumor after 3 days

What is about 71 people?