Question 73166
Exponential growth rate for a product is 10% per year. Using the exponential growth function(N=N0e^rt) with r as growth rate, t as number of years since 1995 and N0 as demand in 1995, when will the demand be double that of 1995?
:
Let the demand (No) = k, then double the demand (N)= 2k, r = .1 (decimal of 10%)
:
No(e^rt) = N
k(e^.1t) = 2k; find t
:
Divide both sides by k:
e^.1t = 2
:
Find the natural log of both sides: remember the nat log of e is 1, so we have:
.1t = ln(2)
.1t = .693147
t = .693147/.1
t = 6.93 years, call it 7 years (2002)
:
:
Check our solution using No = 10
10(e^(.1*7)= 
10(e^.7) =
10(2.01) = 20 = N
:
Did this make sense to you?