Answer:
=69805
Step-by-step explanation:
This is an exponential growth problem. If the population doubles periodically, it follows a law like this:
P(t) = P(0)e^kt
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 = 2183.
Since the population doubles every 28 years, we can write
P(t+28) = 2P(t)
P(0)ek(t+28) = 2[P(0)e^kt]
Simplifying,
e²⁸k = 2
k = ln(2) / 28 = 0.02475 years-¹
Finally,
P(t) = 2183e⁰.⁰²⁴⁷⁵t, t in years
P(t)= 2183e^0.02475t, t in years
Then at t=140 years from now,
P(140) = 2183e⁰.⁰²⁴⁷⁵×¹⁴⁰
P(140) = 2183e^(0.02475 × 140) = 69804.61168
=69805
