Question

The number of compact discs N purchased each year, in millions, can be

approximated by the function

N(t) = 384(1.13)

where t is the number of years since 1991.

After what amount of time will two billion compact discs be sold?


What is the doubling time for the number of compact discs sold in one year?

Answer 1

126.5 years

Explanation:

N(t) = 384(1.13)^t

2,000,000,000 = 384(1.13)^t

(1.13)^t = 2,000,000,000/384

log [(1.13)^t) = log (2,000,000,000/384)

t × log 1.13 = log (2,000,000,000/384)

t = [log (2,000,000,000/384)]/(log 1.13)

t = 126.5