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Given the first term at t₀ is 6 and the second term at t₃ is 32, let's take rabbit population as a function of time to be:
y = abˣ
where y is the population at time x and a the initial population at t₀
32 = 6b³
b = 1.75
Now we replace b in the population function:
y = 6(1.75)ˣ regression for the rabbit population as a function of time x.
The exponential function in terms of base is usually expressed as:
A = A₀e^kt
Hence, the regression equation in terms of base e is:
We substitute en last function, y - value with any number higher than 10,000 to estimate the time for the rabbits to exceed 10,000.
Hence, it takes approximately 13.3 months for the population to exceed 10000
