<PRE><B>Question 821723</B>
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f(t)= P*e^(tk)
where:
P = initial value
k = growth or decay factor per unit of time
t = time
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f(0) = P = 6500
f(t)= 6500*e^(tk)
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f(2) = 6500*1.35 = 8775
8775 = 6500*e^(2k)
8775/6500 = e^(2k)
ln(8775/6500) = ln( e^(2k) )
ln(8775/6500) = 2k
k = ln(8775/6500)/2
k = 0.1500523 growth factor per hour
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time to triple the population:
f(t)= 3*6500 = 6500*e^(tk)
3 = e^(tk)
ln(3) = ln( e^(tk) )
ln(3) = tk
t = ln(3)/k
t = 7.3215293
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answer:
time to triple the population = 7.3 hours = 7 hours and 19.3 minutes
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