Question

2. Answer each of the following based on the scenario below.

Scenario: You bought a brand new iphone 13 for $1,200. Unfortunately your phone
loses 10% of its value every year.
a. Does this scenario represent exponential growth or decay? De
b. What is the initial value of your phone? 2000
c. What is the growth/decay factor? 10
d. Create a function in exponential form that models how much your phone will be worth
after x years.
f(x) =
e. After 3 years how much will your phone be worth?
. After 8 years how much will your phone be worth?

Answer 1

a) losing value is exponential decay.

b) Initial value is the price you paid = $1,200

c) decay factor is 100% - the percent lost per year = 90%

d) value = starting value x decay factor^ time

f(x) = 1200 x 0.90^x

e) replace x with 3 then 8 and solve:

f(3) = 1200 x 0.90^3 = 874.80

after 3 years it is worth $874.80

f(8) = 1200 x 0.90^8 = 516.56

after 8 years it is worth $516.56