Answer
a) It will take 3.54 years for the turtle population to hit 300 female turtles.
b) There will be 78,125 female turtles in 7 years.
Step-by-step explanation
The model has been give to us as
T(t) = 5ᵗ
where
T(t) = Female turtle population at any time t
t = time in years
First part of the question asks us to find when the turtle population will hit 300 female turtles. That is, find t when T(t) = 300
T(t) = 5ᵗ
300 = 5ᵗ
We can rewrite this as
5ᵗ = 300
We will take the natural logarithms of both sides
In 5ᵗ = In 300
t (In 5) = In 300
t (1.6094) = 5.7038
Divide both sides by 1.6094
t = (5.7038/1.6094)
t = 3.54 years = 3 years, 6.5 months
For the second part of the question, we want to calculate the number of female turtles when t = 7 years
T(t) = 5ᵗ
T(7) = 5⁷ = 78,125 female turtles
Hope this Helps!!!