# Calculous Pre

A population grows from 11,000 to 15,000 in three years.

Assuming the growth is exponential, find the growth rate and continuous growth rate

Growth rate ______ %?

Continuous rate _________ %?

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1. I guess by growth rate you mean with yearly compounding and continuous means e^kt

if yearly for three years
15 = 11 (1+r)^3

1.3636 = (1+r)^3
log 1.3636 = 3 log (1+r)
1+r = 1.1089
so
r = .109 = 10.9 percent

now if continuous
1.3636 = e^3k
ln 1.3636 = 3 k
k = .103 or 10.3 percent continuous compounding

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posted by Damon

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