A growth rate equation has a general form of:
f(x) = P (1 + r)^x
Where,
P = present value
r = rate of growth
x = number of years
If we write the given equation on that form, it would be:
f(x) = 4 (1 + 3)^x
Therefore we can see that the population’s growth rate is
300% per year. To make this formula to an equivalent of three times a year (3x),
we have to find the new r.
f(x)_3 = 4 (1 + r)^3x
To calculate this, we must take note that the expression or
value of (1 + r)^x must be constant. Therefore equate this with 4^x.
(1 + r)^3x = (4)^x
Taking the logs of both sides:
3x log (1 + r) = x log 4
Cancelling x:
3 log (1 + r) = log 4
3 (1 + r) = 4
1 + r = 4/3
r = 0.33
Therefore the new growth rate is 0.33 or 33%. (ANSWER)
And, the new correct function is:
f(x)_3 = 4 (1 + 0.33)^3x
or
f(x)_3 = 4 (1.33)^3x (ANSWER)
