4.5 Applications of Exponential Functions 2/8/2013.

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Presentation transcript:

4.5 Applications of Exponential Functions 2/8/2013

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.

Compounding Interest Formula

An amount of $1, 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

Depreciation Formula

If you purchase a BMW for $45,000, the value of the car depreciates by 16% each year. How much will the car be worth in 8 years? V = $45,000 r =.16 t = 8 yrs

Exponential Growth Formula

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)

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

Exponential Decay Formula (half- life)

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

Homework: WS 4.5 do ALL