Question

The population of Adamsville grew from 7,000 to 12,000 in 5 years. Assuming uninhibited exponential growth, what is the expected population in an additional 5 years?

Answer 1

We have that if we assume standard exponential growth, the equation of the population will be:$7000*e^{kt}$ if we start counting from the moment that the population was 7000. We are given that 7000* $e^{5k}$=12000, namely that P(5)=12000 and we need to find $7000e^{(5+5)k}=7000e^{10k}$. Since e^(10k)=e^(5k)*e^(5k), and since we can solve for e^(5k) from P(5), we have:
e^(5k)=12000/7000 and we can calculate P(10). P(10)=7000$\frac{12000^2}{7000^2}$= 20571 people.