Problema Solution
Assume a population P behaves exponentially with time t.
If P decreases by .06% in 5 minutes, by what percent does it decrease in one hour?
Answer provided by our tutors
let
P(0) = C, the start moment t = 0 minutes, C = constant
after 5 min
P(5) = P(0) - 0.06*P(0) = 0.94* P(0)
P(10) = 0.94* P(5) = 0.94*0.94* P(0) = (0.94)^2 * P(0) = (0.94)^(10/5) * P(0)
P(15) = 0.94* P(10) = 0.94 *(0.94)^2 * P(0) = (0.94)^(15/5) * P(0)
we conclude that
P(t) = (0.94)^(t/5)* P(0)
1 hour = 60 min and 60/5 = 12
P(60) = (0.94)^(60/5)* P(0) = 0.94^12* P(0)
P(60) = 0.4759 * P(0)
the decrease is P(0) - 0.4759 * P(0) = 0.5241 P(0) thus the decrease percentage is
0.5241 * 100 = 52.41%
in 1 hour the population will decrease by 52.41%.