Modeling Exponential Functions I. Writing Exponential Growth/Decay Equations from Stories. A) Basic function: y = a(1 ± r)t 1) a = the initial amount. 2) r = the % increase or decrease (written as a decimal). a) Increase means (1 + r) b) Decrease means (1 – r) 3) t = time (read the story for time units, years, hrs, etc.) 4) y = the amount after time has passed.

Modeling Exponential Functions Examples: 1) In 1996 there were 2573 computer viruses. During the next 7 years, the number of viruses increased by about 92% each year. Write a model of this. y = a(1 ± r)t  y = 2573 (1 + .92)t  y = 2573 (1.92)t In what year will the amount exceed 125,000 viruses? Plug the equation into y = on the graphing calculator and look at the table. Sometime during the 5th year it exceeded 125,000 viruses. Answer: In the year 2001

Modeling Exponential Functions Examples: 2) A new 4 wheeler costs $4200. Its value decreases by 12% each year. Write a model for this situation. y = a(1 ± r)t  y = 4200 (1 – .12)t  y = 4200 (.88)t How much is the 4 wheeler worth after 3 years? Plug the numbers into the equation on the graphing calculator and evaluate. Answer: 4200 (.88)3 = 2862.18 It is worth $ 2862.18