Precalculus -- Exponentials and Logarithms

Exponential Functions

100

The growth rate for

f(x)=14*(1.3)^x (as a percentage).

What is 30%?

200

The range of the function 

f(x)=3(7)^x-2 

What is y>-2?

300

The domain of the function

f(x)=4*5^x

What is All Real Numbers?

400

The inverse of the function 

h(x)=4*5^2x

What is h^-1(x)=0.5(log₅(x/4))?

500

The transformations performed on the parent function f(x)=5^x that result in the below function. 

g(x)=4*5^2x+1

What are a vertical stretch, a horizontal compression and a vertical shift?

Logarithms

100

log₁₂(144)

What is 2?

200

log₄(x)=0

What is 1?

300

log_x(64)=3

What is 4?

400

The solution to 

log_x4x=3

What is 2?

500

The logarithmic expression as a single logarithm

2log₁₀(x) + 6log₁₀(y) - 4log₁₀(z)

What is log₁₀(x²y⁶/z⁴).

Solving Equations

100

The solution to 5^x = 1/125

What is -3?

200

The solution to 3^x+12=21

x=2

300

The solution to 

log₃(x+2)=log₃(2x-6).

What is x=8?

400

The solution to 

5ln(2x)=20

What is x = e⁴/2?

500

The solution to 

log₃9 + 2 = 2log₃(x-1)

What is 10.

Applications

100

The scale used to measure the magnitude of earthquakes.

What is the Richter Scale?

200

The period of time it takes for 50% of a substance to decay.

What is half-life?

300

The balance in an account after 5 years if $500 was invested at 5% interest compounded continuously.

What is about $642?

400

The amount of time needed for an investment of $1000 to double if earning 6.25% interest compounded continuously.

What is about 11 years?

500

The distance (d) a tornado traveled based on speed (s) if s(d) = 93logd+65 and the tornado was traveling 220 miles per hour.

What is about 46.4 miles?

Random

100

The ratio of the change in outputs over the change in inputs over a given interval.

What is Average Rate of Change?

200

True or false: Logs are inverses of trees. 

False

300

This phenominal figure, which our days will soon revolve around, can be derived using right triangles and trigonometry.

What is the Unit Circle?

400

True or False: Sohcahtoa is a famous mathematician who studied right triangles.

False.

500

The solution to 

9^log₉(5x)=500.

What is 100?