MATH 101 Chapter 4 Review

Inverse Functions

100

f(x)=x³+1

f^-1(x)=(x-1)^1/3

200

f(x)=x/3

f^-1(x)=3x

300

f(x)=(x-1)²

f^-1(x)=(x)^.5+1

400

f(x)=e^x

f^-1(x)=ln(x)

500

f(x)=log₃(x+2)

f^-1(x)=3^x-2

Log Properties

100

log_b(x)+log_b(y)

log_b(xy)

200

b^log_b^(x)

x

300

log₂(x)=3

x=8

400

log(x³)

3log(x)

500

log(x²-1)-log(2y)

log[ (x²-1)/2y ]

Natural Log

100

ln(e^1/3)

1/3

200

ln(x)-ln(y³)

ln(x/y³)

300

ln(e)

1

400

e^ln(3x)

3x

500

ln(3)=x

e^x=3

Compound Interest

100

How much time will it take to double an initial deposit of $4,000 if the account is compounded continuously at a rate of 5.75% ?

12.05 years

200

What is the interest rate if an account starts with a deposit of $8,500 and after 5 years the account has $10,000? Assume continuous compounding.

3.25%

300

An account has an interest rate of 6% and is compounded annually. If the initial deposit is $1,500, what is the total amount in the account after 5 years?

$2007.34

400

An account has 3.25% interest and an initial deposit of $1,500. What is the total amount in the account after 5.5 years? Assume continuously compounded interest.

$1793.58

500

The equation for continuously compounded interest is A(t)=Pe^rt 

What is the equation for discretely compounded interest?

A(t) = P(1+r/n)^nt

Other Applications

100

pH=-log(H⁺) where H⁺ is the concentration of hydrogen ions.

find the pH of a solution with an H⁺ of 10^-4

4

200

The brightness of a star is modeled by the following formula

B = -log_2.5(I/I₀) where B is the brightness, I is the energy intensity, and I₀ is the baseline intensity.

If the star Spica has a brightness of 1, find the energy intensity (leave in terms of I₀)

2.5I₀

300

The brightness of a star is modeled by the following formula

B = -log2.5(I/I0) where B is the brightness, I is the energy intensity, and I0 is the baseline intensity.

The star Sirius has a brightness of -1.46. Find the energy intensity of Sirius.

I₀2.5^-1.46