Answer:This is an exponential growth problem. If the population doubles periodically, it follows a law like this:
P(t) = P(0)ekt
where P(0) is the initial population at time t=0, and k is a constant with units of years-1.
To find k, let t=0. Then P(t) = P(0) = initial population = 5000.
Since the population doubles every 12 years, we can write
P(t+12) = 2P(t)
P(0)ek(t+12) = 2[P(0)ekt]
Simplifying,
e12k = 2
k = ln(2) / 12 = 0.0577623 years-1
Finally,
P(t) = 5000e0.0577623t, t in years
Then at t=48 years from now,
P(48) = 5000e(0.0577623 * 48) = 80,000
Explanation: