Build the equation
Growth/Decay
Word Problems
Word Problems
Continuous Compounding
Population Models
Mix Bag
100
An endangered population of penguins were recorded in 2002 as having 12494 penguins. Since then, the population has been in decline by 11% since then.
y=12494(1-0.11)^x
y=12494(0.89)^x
100
2243
100
$4000 principal, 5.25% interest rate, compounded continuously
build the equation
A=4000(e)^.0525t
100
Rabbits are multiplying at an alarming rate in the colonial outback of mid-19th century Australia. Describe the initial population amount and the rate of growth of the model
P=16575(1.69)^t
Initial population 16,575 and rate of 69% growth
100
What is the initial amount and growth rate (as a percent) for the function f(x)=2(3)x
initial amount=2 and 200% growth rate
200
Your high-yield savings account has $2500 in it and is accruing interest at a rate of 8.5%.
y=2500(1.085)^x
200
What will be the cost in 17 years?
$32,313.27
200
$17500 principal, 2% interest rate, compounded continuously
build the equation
A=17500(e)^(.02t)
200
Wolf population was on the decline in Yellowstone National Park since 1941 by a rate of 14% decay. If the initial population was 172 wolves, build a population model.
P=172(1-0.14)^t
P=172(0.86)^t
200
Becky invested $19,800 in a certificate of deposit (CD) that pays an annual interest rate of 5.3%. The CD is set to compound yearly. How much is in Becky’s account after 9 years?
A=19800(1+0.053)^9
$31,515.23
300
Your brand new car cost $64000. It is projected to depreciate in value on average 21% over the next several years.
y=64000(1-0.21)^x
y=64000(0.79)^x
300
16,941 people
300
$2565 initial investment, decreasing at a rate of 21.5%, compounded continuously
build the equation
y=2565(e)^(-0.215t)
300
Wolf population was on the decline in Yellowstone National Park since 1941 by a rate of 14% decay. If the initial population was 172 wolves, build a population model.
Using the same model, predict the population in 1961 (20 years later) (round to the nearest wolf)
P=172(0.86)^20 approx 8 wolves
300
What is the decay "b" factor, if DJ's soccer ball depreciates 9% every day he uses it?
0.91
y=(0.91)^x
400
In 1900, there were 1.6 billion people on earth, and throughout the 20th century, global human population grew every year by 1.6%
y=1600000000(1+0.016)^x
y=1600000000(1.016)^x
400
Is the function exponential growth or decay?
Write the equation to represent the graph. 
Decay
y = 2400 (0.5x)
400
Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?
y=10000(e)^(.03t) approx $ 12,712.49
400
Climate change is driving a decimation of biodiversity worldwide. Current models see that of the 1,700,000 known species, we will see a loss of 7% of them each decade. Make a population model P in terms of t decades.
P=1700000(0.93)^t
400
Due to a severe drought, a population of lions is decreasing at a rate of 3.5% per year. Scientists have noticed 80 lions in the area. After how many years will this population of 80 lions drop below 15 lions if this rate decrease continues?
47 years
80(0.965)^t = 15 t approx 46.9
500
Over each period of time, Carbon-14 loses half (or 50%) of its mass. Let's say you are starting with 20 mg of it.
y=20(1-0.5)^x
y=20(0.5)^x
500
If you put $500.00 into an account and the account earns a 3% yearly interest rate. How much will be in the account after 5 years?
Round the nearest cent!
$579.64
500
Bank Zilban offers 5.9% compounded continuously. If you initially deposit $100, how long will it take for your account to reach $500? Round up to the nearest whole year.
y=100(e)^(.059t)=500, t approx 27.2 so 28 years
500
Bacteria reproduces through cell division. If a microbial sample of E. coli weighing 231 grams doubles every hour, write a model of it AND predict its weight after 6 hours.
y=231(2)^6 = 14784g
500
Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?
7 years
10643.01 = 7500(e)^(.05t) t approx 7