Question

The number of magazine subscriptions sold for a student fundraising event has been declining at an annual rate of 12%. If there are currently 983 magazine subscriptions, how long ago, to the nearest tenth of a year, were there 2,521 magazine subscriptions?

A 2.3 years
B) 3.2 years
C)7.4 years
D) 8.3 years

Answer 1

7.4 years

Explanation:

declining at rate of 12% a year is same as saying the rate year upon year is 0.88%.

call n our number of years between 983 subs and 2521 subs.

if we go back n years, our current number of subs was 2521.

we need to find how far in the future will there be 983 subs.

use the formula for 'compound growth and decay.'

that is N = A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

we have 2521 (0.88)^n = 983.

divide both sides by 2521:

0.88^n = (983/2521)

take logarithms of both sides:

log 0.88^n = log (983/2521). simplify by bringing down the n:

n log 0.88 = log (983/2521)

divide both sides by log 0.88:

n = (log (983/2521)) / log 0.88

= 7.37

= 7.4 years (to nearest tenth of a year)