Test Review: Exponential Functions and Logarithms

Name: ______Date:______

Test Review: Exponential Functions and Logarithms

1)  Find the growth / decay rates for growth factors listed below:

a) 3.25 b) 0.025 c) 1.006 d) 0.845

2) State the growth factor for the percent increase or decrease stated below:

a) 22% increase b) 5.6% increase c) 9.8% decrease

3) What is the growth factor for exponential growth functions?

4) What is the growth factor for exponential decay functions?

5) What is the general equation for all growth functions that:

A) Contain the word continuous

B) That are compounded something other than continuously or annually

C) That contain neither the word continuous nor compounded

6) Create a word problem for each of the equations shown below:

a) b) c)

7) Assume you purchased a baseball card for $1800.00 that appreciates 5.4% every year:

a)  What will the value of the card be in 6 years from the date of purchase?

b)  What will the value of the card be in 3 months from the date of purchase?

c)  What will the value of the card be in 15 weeks from the date of purchase?

d)  When would the card have a value of $9,000.00 from the date of purchase?

8) Suppose that you purchased a car for $20,000. This car depreciates at a rate of 20% each year:

a)  What will the value of the car be in 6 years from the date of purchase?

b)  What will the value of the car be in 6 months from the date of purchase?

c) When will the car have a value of $10,000?

9) You just purchased an autographed swimsuit calendar of Mr. Baron (no Speedo’s please). This rare piece of art was bought for $500 and has been compounding monthly at a rate of 6.2%:

a)  What is the calendar worth 20 months after the date of purchase?

b)  What is the calendar worth 3 years after the date of purchase?

c)  What is the calendar worth 2 years before the date of purchase?

d) When will the calendar have a value of $950.00

10) An experiment begins with 6000 bacteria and has been growing continuously at a rate of 8.25% every hour:

a)  How many bacteria are there 5 hours after the experiment begins?

b)  How many bacteria are there 3 days after the experiment begins?

c)  How many bacteria were there 4 hours before the experiment began?

d)  How many bacteria were there 2 days before the experiment began?

e)  When will there be 200,000 bacteria?

11) Carbon 14 (C14) has a half life of 5730 years. This means that ½ of the radio active carbon will decay every 5730 years. Suppose that a sample was found that contains 40 grams of C14:

a)  How may grams of C14 will there be two half-lives from now?

b)  How many grams of C14 were there 2 half-lives ago?

c)  How many grams of C14 will there be 10,000 years from now?

d)  How many grams of C14 were there be 1,000,000 years ago?

e)  What percentage of the C14 will remain in 20,000 years?

f)  What percentage of the C14 was there 30,000 years ago?

g)  When will there be 25 grams? (give the answer in ½ lives)

h)  When was there 150 grams? (give the answer in ½ lives)