Linear vs. Exponential
You have 20 dollars iTunes gift cards. You decided to buy some songs for 1 dollar per song.
Linear
What is the formula for exponential growth?
y=a(1+r)t
The first year of a charity walk even had an attendance of 500 people. The amount of people that attended increased at a rate of 5% each year. How many people will attend the 10th year of the charity walk?
815 people will attend the charity event in 10 years.
f(x)=3(7)x
x=2
f(x)=147
In the equation y=abx
What does b represent?
FACTOR
You wake up with 2 chicken pox and each day the number of chicken pox you have triples.
Exponential
Is this exponential decay or growth? Why?
y=500(.73)5
Decay because inside the parenthesis is less than 1
Find a bank account balance if the account starts with $100, has an annual rate of 4% and the money left in the account for 12 years?
100(1+.04)12= $160.10
(2/5)x
x=4
f(x)=.0256
In the equation y=abx
What does a represent?
y-intercept
Your cellphone plan is 25 dollars a month plus 10 cents for each minute over your allowance
Linear
What is the formula for exponential decay?
y=a(1-r)t
Each year a local country club sponsors a tennis tournament. Pay starts with 128 participants. Each round half of the players are eliminated. How many players will there be after 5 rounds?
4 players
f(x)= -2(4)x
x=3
f(x)= -128
In the equation y=abx
What does x represent?
Exponent
The population of a large town in Minnesota was 273,000,000 in 1998. The population grew 0.6% each year. What will be the population of the town in 2008?
289,829,411 people will live in the town in 2008.
Growth
A city's population is increasing by 5% every year, and there are currently 39,000 people. What will the population be in 2 years?
42,998 people
f(x)=3x
x=-2
f(x)=.11111 or 1/9
y=2(1.03)3
What does 1.03 represent and what is the percent?
Growth Factor and 3%
Monthly car sales of the Mercedes Benz A Class Sedan are $350,000 and decreasing at a rate of 3% per year. What will the value of the car be in 6 years?
$291,540.20 Growth
If the number of bacteria in a colony doubles every 25 hours and there is a current population of 10,000 bacteria, what will the population be 75 hours from now?
80,000 bacteria
y=3(1/4)x
x=5
.003
y=2(.70)x
What does .70 represent and what is the percent
decay factor and 30%