SOLUTION: Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day. Consider an initial population of 200 rabbits. Find the exponential growth functi
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Question 593293: Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day. Consider an initial population of 200 rabbits. Find the exponential growth function.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The exponential growth function is
where N(t) is the population at time t, is the initial population and k is the growth constant (some positive number in the interval [0,1])
In this case, the initial population is 200, so
So the function then becomes
The growth rate is 11.7% per day, so when , the population is now 200 + 0.117*200 = 223.4
So this means we have the equation
Let's solve for k
So the growth constant is approximately
Therefore, the exponential growth function is
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