To solve the population growth problem, we need to use the compound growth formula, which can be written as:
[tex]\[ P = P_0 (1 + r)^t \][/tex]
In this formula:
- [tex]\( P \)[/tex] is the population at the end of the period.
- [tex]\( P_0 \)[/tex] is the initial population.
- [tex]\( r \)[/tex] is the growth rate per period.
- [tex]\( t \)[/tex] is the number of periods.
In our specific problem:
- The initial population ([tex]\( P_0 \)[/tex]) is 10,000.
- The annual growth rate ([tex]\( r \)[/tex]) is 0.08 (or 8\%).
- The number of years ([tex]\( t \)[/tex]) is 20.
Let's plug these values into the formula:
[tex]\[ P = 10,000 (1 + 0.08)^{20} \][/tex]
[tex]\[ P = 10,000 (1.08)^{20} \][/tex]
Therefore, the equation that would be used to calculate the population of the town in 20 years is:
[tex]\[ P = 10,000 (1.08)^{20} \][/tex]
So the best answer from the choices provided is:
D. [tex]\( P = 10,000 (1.08)^{20} \)[/tex]
