SOLUTION: I have been trying to figure out the word problem below for a while and can't understand what numbers to plug into the function to solve. Exponential growth rate for a product i

Question 73166: I have been trying to figure out the word problem below for a while and can't understand what numbers to plug into the function to solve.
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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?

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