Algebra 2 word problem

Question

From 1960 to 1990, the annual percentage increase in the production of CD's was fairly constant. In 1960 production for PopRock company was 40 CD's per year, by 1990 PopRock company was producing 40,000 CD's per year. Model the production with an exponential function P=abtP=abt, where t is the number of years since 1960, a is the production of CD's in 1960 and P is the annual production. 

b=b=

P=P=

You need to solve using logarithms. You must show work for each step to get credit.

Answer 1

The exponential function is:

P = a b ^t We need to find b. In 1990, after 30 years, we have the production 4000 Cd's, so:

4000 = 40 b^30 Now divide both sides by 40:

100 = b^30 To solve this equation we need to get log (with base 10) from both sides:

log 100 = 30 log b

2 = 30 log b

log b = 1/15 so by definition of log we have:

b = 10^(1/15)

b = 1.1659 Then the function is:

P = 40(1.1659)^t In which a = 40 and b = 1.1659.