Question

you purchase a new car a $31,000 and the value decreases %30 each year. How many years will it take before your car is worth lass than $24,000? less than $5,000?

Answer 1

i figured out the function of the value of the car would be 31,000(.70)^t

Answer 2

a) 31,000(.70)^t = 24,000
b) 31,000(.70)^t = 5,000

Answer 3

yea i got that but i dont know how to find t where its less than $5000

Answer 4

take the log of both sides.
log(31,000(.70)^t) = log(5,000)
log(31,000)+log(.7^t) = log(5,000)
t log(.7) = log(5,000)-log(31,000)
t = (log(5,000)-log(31,000))/log(.7)

Answer 5

ohh okay so u want to get the t on one side..so t will equal -.938 (rounded) but how will it be less than 5000 at negative.938 years?

Answer 6

t should be 5.115

Answer 7

t = (log(5,000)-log(31,000))/log(.7)
= log(5/31)/log(.7)

Answer 8

ohh okay thought it was 7 not .7 log srry k i get it know so that means at 5.115 years its value is less thank 5000?

Answer 9

at 5.115 years its value is equal to 5000
beyond 5.115 years, its value will be less than 5000
so after 6 years, its value will be less than 5000

Answer 10

okay thank u soo much...helps me 4 my upcoming exam

Answer 11

:)