Answer
The population would reach 1 million after over $44$ years.
Work Step by Step
The population of Glenbrook is 375,000 and is increasing at the rate of $2.25%$ per year.
So, after the first year, its population is $375000+375000\times0.0225=375000\times1.0225$.
After the second year, the population is $375000\times(1.0225)^2$
Therefore, if we continue like that and call the population of Glenbrook after $t$ years $p$, we can come up with the model to calculate it:
$$p=375000\times1.0225^t$$
For the population to reach 1 million, meaning to find $t$ so that $p=1000000$:
$$375000\times1.0225^t=1000000$$ $$1.0225^t=\frac{8}{3}$$
- Take the $\log_{1.0225}$ of both sides: $$t=\log_{1.0225}\frac{8}{3}\approx44.081\approx44(years)$$
The population would reach 1 million after over $44$ years.
