Growth & Decay

Using Exponential Functions

 

Growth and Decay Word Problems

This equation is used to represent a variety of growth and decay word problems—depending on the type of problem b will change

y = ending amounta = initial amountt = time (time number of time cycles)b = base growth (1 + r) (where r =

rate)decay (1 – r)half-life (.5)doubles, triples, etc. (2,

3,etc.)

taby

Examples

The population of Pasadena in the year 2000 was 142,000 people. Assume that the population is increasing at a rate of 2.25% per year. What will the population be in the year 2030? in 2050?

Examples

The population of Leonardville in 1890 was 89,000. Assume the population is decreasing at a rate of 2.75% per year. What was the population in 1920? in 1930?

Examples

The population of Bernadetteton in 1985 was 560,000. If the population is increasing at a rate of 3% each year, when will the population reach a million?

Examples

The half-life of Howardium-234 is 25 days. If you start with 70 grams initially, how much is left after 100 days? after 400 days?

Examples

The half-life of Sheldonium-14 is 5730 years. If you start with 600 grams initially, how much do you have left after 34,380 years?

Examples

Amy Farrah Fowler purchased a house in 1990 for $100,000. The annual rate of appreciation is 3.25%. How much will the house be worth in 2010?

Compound Interest

p=initial investmentr=interest raten=# of times

compounded in a year Annually n=1 Monthly

n=12 Quarterly n=4 Weekly

n=52 Bimonthly n=24

t=time in years

nt

n

rpy

1

Compound Interest Example

Raj invests $500 into an account earning 7% annual interest compounded monthly. When will his investment be doubled?

Compound Interest Examples

Stuart invests $3500 into an account earning 12% annual interest compounded bimonthly. How much will he have after 7 years?

Compound Interest Examples

Mrs. Wolowitz invested $10,000 into an account earning 3.6% annual interest compounded weekly. How long did it take for her account to reach $12,000?

Continuously Compounded Interest

p=principal (initial investment)e=ex2.71…r=interest ratet=time

rtpey

Continuous Compounding Example

Penny invests $23,000 into an account earning 6.2% annual interest compounded continuously. How much will she have after 6 years?