Answer
a. See table and explanations.
b. $a_n=20.85(1.02)^{n-1}$
c. $30.98$ million.
Work Step by Step
a. See table. The first column is the year, the second column is the population in millions, the third column is the ratio of a population to that of the preceding year, and the last column is the ratio rounded to two decimal places. We can see that Texas has a population increase that is approximately geometric with $r\approx1.02$ (except for the last data point).
b. With $a_1=20.85, r=1.02$, we can write the general term as $a_n=20.85(1.02)^{n-1}$, where $n$ is the years after 1999.
c. For year 2020, we have $n=2020-1999=21$. Thus, we have $a_{21}=20.85(1.02)^{21-1}\approx30.98$ million.
