Answer
After around 19 years, the population of Knoxville would reach 1 million.
Work Step by Step
Here is what we have:
- The population of Knoxville currently.
- The annual increase rate.
So to calculate the population of Knoxville at a given time in the future, we would design an exponential model like this:
$$p = p_n(1+r)^t$$
$p_n$: the population of Knoxville currently $(p_n=500.000)$
$r$: annual increase rate $(r=3.75\%=0.0375)$
$t$: the amount of time which has passed from now until the estimated time in the future (years)
$p$: the population of Knoxville after time $t$ that we are estimating
Here, as you can see, we need to find when the population would reach 1 million, which in essence is to find $t$ so that $p=1.000.000$
To find $t$, we substitute the known values:
$$500000(1+0.0375)^t=1000000$$
$$500000\times1.0375^t=1000000$$
$$1.0375^t=2$$
Here, we use graphing calculator and find out that $t\approx18.828\approx19$ (years)
Therefore, we can conclude that after around 19 years, the population of Knoxville would reach 1 million.
