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Natural Log Word Problem

Let N(t) represent the number of hits at the end of t months and assume continuous exponential growth. Then the initial number N_{0} is 125 hits and the number of hits N after a time of 3 months, is 2000. Find the continuous growth rate K.

Website Traffic:

Month # of hits
Jan 125
April 2000

 

Exponential Growth Formula:

  • N(t)=N_{0}e^{kt}

N(t)=2000

N_{0}=125

t=3

\frac{2000}{125}=\frac{125}{125}e^{t(3)}

16=e^{3k}

ln(16)=ln(e^{3k})

\frac{ln(16)}{3}=\frac{3k}{3}

k=\frac{ln(16)}{3}

k\approx 0.924

92.4%\ per\ month

N(t)=125e^{0.924t}