Problema Solution
A population is 40,000 in year t=0 and declines at continues rate of 6% per year.
a) find a formula for p(t), the population in year t.
b) by what percent does the population decrease each year? Why is this less than 6%?
Answer provided by our tutors
a)
p(0) = 40,000
p(1) = 40,000 - 0.06*40,000 = 0.94*40,000
p(2) = 0.94*p(1) = (0.94^2)*40,000
p(t) = (0.94^t)*40,000
b)
lets calculate the decrease between year t=k and t=0
p(0) = 40,000
p(k) = (0.94^k)*40,000
(40,000 - (0.94^k)*40,000)/40,000 = 1 - (0.94^k) which is not the same as 1 - 0.94 = 0.06 (when the decrease is 0.06%)
0.94^k < 0.94
1 - 0.94^k > 0.94
the decrease is more then 6% compared to the start year when t=0.