Question

Bellville has a population that can be modeled by the equation y=25e^0.015x, in which x is time in years and y is the population in thousands. Hilltown has a population that can be modeled by the equation y=10e^0.022x, in which x represents time in years and y represents the population in thousands. In how many years will the two towns have an equal population?

Answer 1

Set 25e^{0.015x} = 10e^{0.022x}.

Divide both sides by 10 and take logs:
2.5 = e^{0.007x} ⇒ ln(2.5) = 0.007x ⇒ x = ln(2.5)/0.007 ≈ 130.9.

So in about 131 years the populations will be equal.