Question

the population of a town can be modeled by the regression equation $y = 20,000(1.03^x)$. which is the best prediction for the population in year 25?
a. 50,002
b. 41,876
c. 34,049
d. 30,252

Explanation:

Step1: Substitute x=25 into equation

Substitute $x=25$ into $y=20000(1.03^x)$:
$y=20000(1.03^{25})$

Step2: Calculate $1.03^{25}$

Calculate the exponential term:
$1.03^{25} \approx 2.09377793$

Step3: Multiply by initial population

Multiply the result by 20000:
$y \approx 20000 \times 2.09377793$

Answer:

B. 41,876