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11-2 Exponential Functions

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11-2 Exponential Functions

Power Function – a function with base x and any real number as the exponent (ex: y=x4)

Exponential Function- function with a positive base and a variable as the exponent (ex: y = 3x)

You can find the equation of an exponential function just like we did for linear.

- Type in data
- Turn on Stat Plot-Zoom 9
- Stat-Calc-0ExpReg

- A cup of coffee is 95°C in a room that is 20°C. The cooling for this cup can be modeled by the equation y=75(.875)t where y is the temperature and t is the time in minutes. Find the temperature after 15 minutes.

Exponential Functiony = a • rt

a = original amount, r = rate t= time

Rate can be several things….

(1 ± %) for growth or decay

(2) For “double”

(1/2) for half life

What is the original amount and how much is each item increasing/decreasing?

- Y=4 (.90)x
- Y=200 (.75)x
- Y=5(1.10)x
- Y=½ (1.50)t

3) Suppose two mice live in a barn. If the number of mice quadruples every 3 months, how many mice will be in the barn in after 2 years?

4) How much will a car be worth in 5 years if you bought it for $20,000 and it depreciates 16% each year?

5) John gets a 2% pay raise every year. If right now he makes $8.00 an hour, how much will he make in 2020?

When kerosene is purified to make jet fuel, pollutants are removed. Suppose a filter is fitted in a pipe so that 15% of impurities are removed for every foot that the kerosene travels.

Write an exponential function to model the situation

About what percent of impurities will remain after the kerosene travels 12 feet.

Will the impurities ever be complete removed? Why/Why not?

A

A- total amount

P-principal (original amount)

R-interest rate

N-number of time compounded each year

- Find the total amount of money in an account at a rate of 5% compounded daily if Mrs. K invest $2000 for 7 years.
- Find the amount of interest charged on a credit card if left unpaid for 3 years if the original amount was $1000 compounded 12% monthly.