Answer:
They'll reach the same population in approximately 113.24 years.
Step-by-step explanation:
Since both population grows at an exponential rate, then their population over the years can be found as:
[tex]\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t[/tex]
For the city of Anvil:
[tex]\text{population anvil}(t) = 21000*(1.04)^t[/tex]
For the city of Brinker:
[tex]\text{population brinker}(t) = 7000*(1.05)^t[/tex]
We need to find the value of "t" that satisfies:
[tex]\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24[/tex]
They'll reach the same population in approximately 113.24 years.
