A PPLICATIONS OF E XPONENTIAL E QUATIONS : C OMPOUND I NTEREST & E XPONENTIAL G ROWTH Math 3 MM3A2

I WANT MONEY, L OTS AND L OTS OF MONEY

C OMPOUND I NTEREST When you have some money that you want to put away for a rainy day, you need to find a bank that will pay you interest.

G ET YOUR MONEY TO WORK FOR YOU. If you put your money in a piggy bank, it won’t grow. Banks will pay you if you let them use your money.

I NTEREST & C OMPOUNDING Periodically, the Bank will give you money, called interest. Each time the bank pays you, it is called compounding. Compounding is like planting money. You make money off of the money that the bank paid you.

H OW DOES IT WORK ? Banks use a formula that is based on how often the account is compounded. Will the frequency of compounding affect the amount of money you earn? Good Question. Let’s see if we can figure that out.

C OMPOUNDING F REQUENCY 1. Annually 2. Semi-Annually 3. Quarterly 4. Monthly 5. Semi-Monthly 6. Weekly 7. Bi-Weekly 8. Daily 1. Once per year 2. Twice per year 3. Four times per year times per year times per year times per year times per year times per year

C OMPOUND I NTEREST F ORMULA : A = final amount P = principal amount (starting) r = rate (percentage) t = time (in years) n = number of times compounded per year

J ORDAN INVESTS $1050 AT 5.5% INTEREST FOR 5 YEARS. H OW MUCH MONEY WILL HE HAVE IF THE INTEREST WAS COMPOUNDED … Quarterly? Monthly?

J ORDAN INVESTS $1050 AT 5.5% INTEREST FOR 5 YEARS. H OW MUCH MONEY WILL HE HAVE IF THE INTEREST WAS COMPOUNDED … Semi-Monthly? Weekly? Daily?

W HICH FREQUENCY IS BETTER ? The more often an account is compounded the better! What does Donald Trump think about compounding interest? It blows him away!

H ERE IS ANOTHER A PPLICATION Bacteria grows at an exponential rate. A = P(1+r) t A population of 3000 bacteria is growing at a rate of 15% per day. After 10 days, what will the bacteria population be? A = 3000(1+.15) 10 A =

H ERE IS ANOTHER A PPLICATION Plutonium decays at an exponential rate. A = P(1 - r) t A population of 5000 bacteria is decaying at a rate of 20% per day. After 5 days, what will the bacteria population be? A = 5000(1-.20) 5 A =

U SE Y OUR C ALCULATOR TO G RAPH THE F OLLOWING EQUATIONS : Notice how the graph decreases This is decay Notice how the graph increases This is growth y = 64(½) x y = 12(3) x W HAT MAKES IT GROWTH OR DECAY ?

G ROWTH OR D ECAY An exponential function in the form y = ab x Represents decay if 0<b<1 Represents growth if b>1 Determine if the following is growth or decay 4(2/5) x 2/3 (5) x 64(7/6) x Decay Growth