The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years
Growth constant
The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor
it is also called the logarithmic return, compounded return, or the force of interest.
Note that the general formula for growth rate is given as;
[tex]P(t) = P0 e^k^t[/tex]
Where,
Po = Initial value = 400 squirrels
r = Rate of growth
k = constant of proportionality = 0. 5 per year
t = time = 1 year
The function P(t) is given as;
P(t) = 400 e^0.5t
Note that the formula for doubling time is given as;
[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]
r = 4
t = 1
substitute into the formula
[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]
Doubling time = 1 × 17. 68
Doubling time = 17. 68 years
Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years
Learn more about doubling time here:
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