SOLUTION: A new motor boat cost $6000. The value of the boat decreases by 15% each year. a) Write a model to describe the situation. Let V be the value of the boat after t years.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A new motor boat cost $6000. The value of the boat decreases by 15% each year. a) Write a model to describe the situation. Let V be the value of the boat after t years.       Log On


   

Question 1070978: A new motor boat cost $6000. The value of the boat decreases by 15% each year.
a) Write a model to describe the situation. Let V be the value of the boat after t years.
V = _(_)x
b) What is the value of the boat after 3 years? (round to two decimals)
V = $_
c) In what year is the value of the boat $2260? (round to the year)
year _

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
The boat loses 15% per year, which is the same as saying the boat's value is 85% of what it was the previous year. So:
a)V=6000(.85^t)
b)V=6000(.85^3)=6000x.614125=$3684.75 as the value of the boat after 3 years.
c)2260/6000=.85^t
.377=.85^t
log .377=log .85^t=t log.85
t=log .377/log .85=6.00788264468 years. ☺☺☺☺