SOLUTION: A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate and and continuous growth rate. Thank you! :D

Question 278305: A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate and and continuous growth rate.
Thank you! :D
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A population doubles in size every 15 years.
Assuming exponential growth, find the annual growth rate and and continuous growth rate.
:
Assume an initial amt of 1, then results are 2
:
Let x = per cent in decimal form growth rate per year
1(1+x)^15 = 2
ln((1+x)^15) = ln(2)
15*ln(1+x) = .693
ln(x+1) =
ln(x+1) = .04621
find the antilog (e^x on calc)
x+1 = 1.0473
x = 1.0473 - 1
x = .0473 or 4.73 % annual growth rate
:
Check on a calc: enter 1.0473^15 = 2.000
:
:
Continuous growth rate
1*e^(15x) = 2
ln(e^15x) = ln(2)
15x*ln(e) = ln(2)
ln(e) = 1 so we have
15x = .693
x =
x = .0462 or 4.62 % growth continuously
;
Check on a calc: enter e^(.0462*15) = 1.99997 ~ 2
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