Exponential growth/decay
The world population in 2000 was about 6.08 billion, growing at 1.26% each year. How many people will there be in 2010?
6.08(1+0.0126)^10
6.89 billion
Markel is baking bread and using yeast. While his yeast activates, the population grows continuously. If there were 1200 yeasts when he started and they grow 2% a minute, how many yeasts will he have when they are fully bloomed in 13 minutes?
1200e^(0.02*13)
1556 yeasts
semiannualy
twice
equation used to find compound interest
a=p(1+(r/n))^(n*t)
what is the continuous compound interest equation
a=Pe^(r*t)
Mark just bought a new car. If he paid $15,000 for it new, and it loses 10% of it's value each year, how much will it be worth in 15 years?
15,000(1-0.1)^15
$3088.36
Daphnee scraped her knee when she accidentally fell getting on the bus to go home. If her cut was 4 cm long, and is healing 3% a day, how small will her cut be in a week?
4e^(-0.03*7)
3.2 cm long
monthly
12
define the variables in the equation
a = total amount
p = staring amount
n = times compounded yearly
r = rate
t = time
Define the variables in the equation
P = initial amount
e is a number
r = rate (as a decimal)
t = time
Amina is studying the local raccoon population. If she has counted 80 raccoons in the neighborhood and noticed the population is decreasing 5% a week, how many raccoons will there be in her neighborhood in a month?
80(1-0.05)^4
65 raccoons
Derivaldo is working on improving his grade in math class. If he started with a 27, and continuously increases his grade 78% a week, what will his grade be in three weeks?
27e^(0.78*3)
280.2 (really good)
quarterly
4
$100 for 3 years, compounded annually at a rate of 10%.
100(1+(0.1/1))^(1*3)
$133.10
$400 at 0.3% for 12 years
400e^(0.003*12) = $414.66
Marcelyn is studying bacteria in the lab. If there are 300 bacteria when she started and the population grows 300% each day, how many bacteria will she have in 4 days?
300(1+3)^4
76,800 bacteria
Roandy is starting a small business selling pencils at school. He started with 100 pencils. If he continuously sells 2% of his pencils each hour, how many pencils will he have in 8 hours at the end of the day?
100e^(-0.02*8)
85 pencils
biweekly
26
$15,000 for ten years at an interest rate of 6% compounded monthly
15,000(1+(0.06/12))^(12*10)
$27,290.95
$12,000 at 90% for half a year
12,000e^(0.9*0.5) = $18,819.75
Ahmari is collecting cool rocks. If he has 40 rocks, how many will he have picked up this week if he picks up 50% of his collection a day?
40(1+0.5)^7 = 683
683-40= 643 rocks picked up this week
Arlydia's family is planning a money gift for her 21st birthday. If they put $10,000 in an account continupusly growing by 2% each year, how much will be in the account on her birthday if they opened it the day she was born?
10,000e^(0.02*21)
$15,219.61
daily
365
You want to invest $20,000 for the next 20 years. You have two options for your investment.
Bank X offers simple interest at a rate of 8%.
Bank Y uses compound interest at a rate of 8% compounded yearly. Which should you choose?
X = 20,000e^(0.08*20) = $99,060.65
Y = 20,000(1+(0.08/1))^(1*20) = $93,219.15
Choose Bank X
You want to invest $5,000 for the next 60 years. You have two options for your investment.
Bank X offers simple interest at a rate of 3%.
Bank Y uses compound interest at a rate of 0.5% compounded daily. Which should you choose?
X = 5,000e^(0.03*60) = $30,248.24
Y = 5,000(1+(0.005/365))^(365*60) = $6,749.28
Choose Bank X