Question

The formula a = 118e^0.024t models the population of a particular city, in thousands, t years after 1998. when will the population of the city reach 140 thousand?

Answer 1

We use the given equation to determine 't' by inputting a value of 'a'. The variable 't' is the time of years that have passed  after 1998. The variable 'a' denotes for the population. I would just like to clarify beforehand that the unit for 'a' is in thousand already so as to arrive at a defined solution. Thus, when we substitute the population of 140 thousand, that would already be a=140. This is because if I substitute 140,000, the equation would become undefined, and therefore, unsolvable.

So, substituting the values:

140 = 118 e^0.024t
140/118 = e^0.024t
Taking the natural logarithm, ln, on both sides,

ln (140/118) = lne^0.024t
ln(140/118) = 0.024t
t = ln(140/118) ÷ 0.024
t = 7.12 years

So, that would be approximately 7 years after 1998. The population would reach 140 thousand in year 2005.