Step-by-step explanation:
The equation of a exponential function with growth is
[tex]y = a(1 + r) {}^{x} [/tex]
Where a is the initial value, r is the growth rate as a decimal, and x is the number of years.
The initial value is 40
R is 0.5, the growth rate
We must find the number of years it take to get 200 rabbits
So y=200
[tex]200 = 40(1 + 0.5) {}^{x} [/tex]
[tex]200 = 40(1.5) {}^{x} [/tex]
Let graph the function in desmos
According to graph, it takes about 3.9 years for the population to grow to 200 rabbits
