6.1 Exponential Growth and Decay Functions

Exponential Growth and Decay Functions Exponential Decay:

Parent Functions for Exponential Growth and Decay Functions

Graphing Exponential Growth and Decay Functions Asymptote: the line that a graph approaches more and more closely Solution: Asymptote: x-axis x -2 -1 1 2 y 3 9

Growth/Decay Equation Suppose the cost of a hamburger increases at the rate of 9% per year and the cost now is $4. Time (years from now) 1 2 3 t Cost (dollars) 4 4(1.09) 4(1.09)2 4(1.09)3 4(1.09)t Cost is shown as a function of time t. y= amount at time t, a = initial amount, r = percent increase or decrease (as a decimal);1+ r = growth factor, 1- r = decay factor, t = time

Example 2 6 days from now ( ): Suppose that a radioactive isotope decays so that the radioactivity present decreases by 15% per day. If 40kg are present now, find the mass present (a) 6 days from now and (b) 6 days ago. 6 days from now ( ): 6 days ago ( ):

Exponential Decay Example 3. A radioactive isotope has a half-life of 4 days. This means that half the substance decays in 4 days. At what rate does the substance decay each day? The daily decay rate is 16%.

Example 4 A certain population grows 50% every year. If this population starts out with 100 members, how many members will there be in 3 years? Solution: Thus there will be 337 members of the population after three years.

Compound interest A= amount after time t. P = Initial principal r = rate in decimal n = number of times compounded in a year. t = time in years This formula can be derived from the Exponential Growth and Decay Formula

Example 5 You deposit $9000 in an account that pays 1.46% annual interest. Find the balance after 2 years when the interest is compounded quarterly. Solution: The balance at the end of 2 years is $9266.18

Example 6 =$5978.09 You invest $5000 in an account paying 6% compounded quarterly for 3 years. How much will be in the account at the end of the time period? P=$5000 r = .06 n = 4 t = 3 =$5978.09

Example 7 What is the amount on the account after $1 is invested for one year at 15% interest compounded monthly? P = 1 r = .15 n = 12 t = 1 =1.1608