1. 8.3 Applications of Exponential Functions 3/25/2013

2. Compound Interest Interest that accrues on the initial principal and the accumulated interest of a principal deposit, loan or debt. Compounding of interest allows a principal amount to grow at a faster rate than simple interest, which is calculated as a percentage of only the principal amount.

3. Compounding Interest Formula

4. An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4%, compounded quarterly. What is the balance after 6 years? P o = $1,500 r =.04 n = 4 (quarterly = 4 times per year) t = 6 yrs Calculator: Follow order of Operations: Do what’s in the ( ), then raise it to the exponent, then multiply by 1500.

5. Exponential Growth Formula

6. Sarah observes that the number of bacteria in the colony in the lab doubles every 30mins. If the initial number of bacteria in the colony is 50, what is the total number of bacteria in the colony after 5 hours? P o = 50 b = 2 t = 5 hrs r =.5 hrs (30mins) Calculator: raise 2 to (5÷0.5) then multiply by 50.

7. Half Life is the amount of time that the substance's total amount is halved.

8. Exponential Decay Formula (half- life)

9. Technitium-99m is a radioactive substance used to diagnose brain, thyroid liver and kidney diseases. This radioactive substance has a half life of 6 hours. If there are 200 mgs of this technetium-99m, how much will there be in 12 hours? P o = 200 mg d = ½ t = 12 hrs r = 6 hrs Calculator: raise 0.5 to (12÷6 or 2) then multiply by 200.

10. Homework: WS 8.3 do ALL