11-2 Exponential Functions. Power Function – a function with base x and any real number as the exponent (ex: y= x 4 ) Exponential Function- function with a positive base and a variable as the exponent (ex: y = 3 x ). Exponential Regression.
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.
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?
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- total amount
P-principal (original amount)
N-number of time compounded each year