Final answer:
The exact growth factor, c, is found by taking the natural logarithm of the ratio of the amount of foxes after 12 years (N12) to the initial amount of foxes (N0) and dividing by the time in years, which gives c ≈ 0.1155.
Step-by-step explanation:
To find the exact growth factor, c, in the exponential growth model Nt = N0ect, given the initial number of foxes N0 is 600 and the number of foxes after 12 years N12 is 2,400, we substitute these values into the model.
Starting with the equation Nt = N0ect and inserting the known values:
2,400 = 600e12c
Dividing both sides by 600 yields:
4 = e12c
Take the natural logarithm of both sides to solve for c:
ln(4) = ln(e12c)
ln(4) = 12c
So, c = ln(4) / 12
Calculating this gives us the value of c:
c = ln(4) / 12
≈ 0.1155