The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

Step-by-step solution

The population growth follows the exponential model P(t) = P₀ e^ kt , where P₀ = 40000 is the initial population. Given that P(20) = 80000 , we substitute to find k : 80000 = 40000 e^ 20k Dividing both sides yields 2 = e^ 20k Taking natural logarithms: (2) = 20k Therefore, k = (2) 20 After 60 years, the population is: P(60) = 40000 e^ 60k = 40000 e^ 3 (2) = 40000 2^3 = 320000 The population after another 40 years will be 320000 .