Question

The population in a city is 650,000 and grows at a rate of 5 percent per year. In approximately years, the population of the city will reach 1 million. (Model the situation as P = P0ert.)

Answer 1

The initial population is P₀ = 650,000.
Growth rate, r = 5% per year, or r = 0.05.

Let t = years.
The proposed model is

`P(t)= P_(0)e^(rt)`
or

`P(t)=650000e^(0.05t)`

Therefore

`(P)/(650000) =e^(0.05t)`
ln(P/650000) = 0.05t

When P = 1,000,000
0.05t = ln(1000000/650000) = 0.4308
t = 8.6157 years = 2 years (approx)

Answer: 2 years (approx)