Exponential Growth
Will exponential growth problems be increasing or decreasing?
Increasing
What is an example of a decay function?
Decrease in value, population decline, radioactive material decreasing, etc.
If something is being compounded quarterly, how often is it happening per year?
Quarterly = 4 times per year
Convert from log to exponent.
log3 27 = 3
33 = 27
Evaluate:
log5 125 = x
Convert to exponent form: 5x = 125
x = 3
"A small island has a population of 850 people. Each year the population grows 1.1%. After 10 years, how many people will be on the island?"
What is the C value?
C = 850 People
Your car was valued at $14,000, but its value decays by 4.5% each year. How much is it worth in 7 years?
What is the value of r?
r = .045
(Remember that it needs to be a decimal for the formula!)
Is compound interest a growth or decay model?
Growth
Convert from exponent to log
43 = 64
log4 64= 3
Evaluate:
log6 216 = x
6x = 216
x = 3
A population of 450 spiders in a house is growing each month at a rate of 4.6%. After 5 months how many spiders are there?
Identify the C, r, and t value of the problem.
C = 250
r = .046
t = 5
(And you should probably just burn the house down.)
You buy a computer worth $1,500. It's estimated to lose 10% of its value each year. After 4 years, how much is it worth?
Identify the C, r, and t values.
C = $1,500
r = .10
t = 4
You borrowed $10,750 for 5 years at 4% interest that is compounded quarterly. How much will you owe in total?
Identify C, r, t, and n values.
C = $10,750
r = .04
t = 5
n = 4
Convert from log to exponent
log2 64 = 6
26 = 64
Evaluate:
log 18 = x
x = 1.255
(Round out three decimal places)
You invest $4,500 into a special savings account with a 2.5% yearly interest rate. After 10 years, how much money is is the account?
Approximately $5,760.38
A population of wolves is released into a wildlife preserve. There is a population of 1,450 deer in the preserve, which the wolves begin to hunt. It is estimated that the population of deer will decrease by 6.4% per year. How many deer are left after 5 years?
Approximately 1,041 deer
You take out a loan for a new car for $19,000. You are given a 2.5% interest rate that will be compounded semiannually for 5 years. How much will you pay back in the end?
Approximately $21,513.15
Convert from exponent to log
62 = 36
log6 36 = 2
Evaluate:
ln 5.6 = x
x = 1.723
(Round out three decimal places)
A particular strain of bacteria doubles every 30 minutes. You start will a single cell of the bacteria. After 3 hours, how many bacteria cells are present?
64 Cells
A tennis tournament is being held with 256 participants. After each round, half of the players are eliminated. How many players remain after 3 rounds?
32 Players
You invest $10,000 into an account with a 3.5% interest rate that is compounded monthly. How much money will be in the account at the end of 7 years?
Approximately $12,771.66
Convert from log to exponent
log64 8 = 1/2
641/2 = 8
Evaluate:
log7 49 = x
7x = 49
x = 2