Mat108 Exam 3 Review part 2

Mostly inverses

100

This is the solution to 3^3x=81.

What is x=4/3?

200

This function, if it exists, is the inverse of f(x)=1/23.

What does not exist?

300

This function, if it exists, is equivalent to (f^-1)^-1.

What is f?

400

This is how we determine if a graph passes the Horizonal Line Test.

What is if every horizontal line intersects the graph at most once?

500

This is the number of x-values each y-value in the range of an invertible function can come from.

What is one?

Compound Interest (exam 2 stuff)

100

John invested $16,000 at 3% compounded annually. This is how much John has after 7 years. 

What is $19,677.98?

200

Jeremy borrowed $96,300 at 3% compounded annually. This is the amount Jeremy owes after 8 years.

What is $121,989.96?

300

Mary borrowed $450 at 8% compounded semiannually. This is the amount Mary owes after 3 years.

What is $569.39?

400

Ken invested $372.28 at 7% compounded quarterly. This is the amount in Ken's investment after 2 years and 8 months.

What is $447.96?

500

Carlos invested $147,000 at 13% compounded monthly. This is the value of Carlos's investment after 5.5 years. 

What is $299,342.20?

Like base equations

100

Let f(x)=5^x. This is the value of x when f(x)=1/5.

What is x=-1?

200

Let f(x)=5^x. This is the value of x when f(x)=25.

What is x=2?

300

This is the solution to 8^x-4=1.

What is x=4?

400

This is the solution to 9^x+4=27

What is x=-5/2?

500

This is the solution to 32^x-2=64^x-3.

What is x=8?

Logarithms

100

This is the logarithmic form of 657=476^x.

What is x=log₄₇₆657?

200

This is the solution to log₂x=4.

What is x=16?

300

This is the solution to log₂x+log_x(x-2)=3.

What is x=4?

400

This is the solution to log(5x)=log(2x+9).

What is x=3?

500

This is the solution set to the equation ln(n²+12)=ln(-9n-2).

What is n=-2,-7?