Question

A cell phone costs $750 and loses 28% of its value each year. What is the value of the phone after 2 years?

1. $216.54
2. $388.80
3. $1228.80
4. $456.30

Answer 1

Initial costs 750 and loses .28 of value each year, so still worth 1-.28=.72 of value at start of next year. 750*(.72)^n is the value after n years since for n=0, new, it is 750*.72^0=750*1=750, and after 1 year it is worth 750*.72^1=750*.72 means it lost 28% value after one year. If you with to express it as an exponential exp(..) you need to convert the .72^n into exp(log(.72)*n)=exp(-.3285*n) so you get

750*exp(-.3285*n) as the value after n years.

Answer 2

388

Explanation:

first year it loses 210

750×.28=210

second year phone value is 540

540×.28=151.2

third year phone value is 388