1. 8.3 Applications of Exponential Functions 3/12/2014

2. Growth by doubling: Bacteria One of the most common examples of exponential growth deals with bacteria. Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. For example, if we start with only one bacteria which can double every hour, by the end of one day how many bacteria will we have? http://www.regentsprep.org/regents/math/algebra/ae7/expdecayl.htm End of Hour 12345678910...24 Bacteria - starting with one 2481632641282565121024...16,777,216 Pattern: 21212 2323 2424 2525 2626 2727 2828 2929 2 10 2 24

3. Compound Interest Interest that builds up on the initial principal and the accumulated interest of a principal deposit, loan or debt.

4. Compounding Interest Formula

5. 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.

6. Exponential Growth Formula

7. 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.

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

9. Exponential Decay Formula (half- life)

10. 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.

11. Homework: WS 8.3 do ALL