# Pre-Calcs

Amount after time t A (t) = yobt

Where:
yo = starting amount
b = growth constant (percent remaining)
t = number of time units

In the 1978 the population of blue whale in the southern hemisphere was thought to number 5000. Since whaling has been outlawed, and an abundant food supply is available the population N(t) is expected to grow exponentially according to the formula N(t) =5000e0.0036t where t is in years and t=0 corresponds to 1978

a) predict the population in the
year 2010
b) how may years will it take the
whole population to exceed
6000?

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N(t) =5000e^(0.0036t)

a) 2010 - 1978 = 32
N(32) = 5000 e^(32(.0036)) = 5610

b)
6000 = 5000 e^(.0036t)
1.2 = e^(.0036t)
ln 1.2 = .0036t
t = ln 1.2/.0036 = 50.6

so it will take 50.6 years from 1978 to reach 6000
so to go over 6000 would take 51 years or in the years 2029

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posted by Reiny

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