Question

The population of a town can be modeled by the regression equation
y = 20,000 (1.03). Which is the best prediction for the population in year 25?
OA. 50,002
OB. 30,252
OC. 41,876
OD. 34,049

Answer 1

Answer:

C) 41,876

Step-by-step explanation:

The population of a town is modeled by the regression equation:

$y = 20000 (1.03)^x$

where:

• y is the population.
• x is the number of years.
• 20,000 is the initial population.
• 3% is the growth rate.

A regression equation models the relationship between an independent variable (x) and a dependent variable (y), and can be used to predict the values of the dependent variable (y) for new or unseen values of the independent variables (x).

To find the best prediction for the population after 25 years substitute x = 25 into the given regression equation:

$y = 20000 (1.03)^{25}\\\\y = 20000 (2.09377792965...)\\\\y=41,875558593...\\\\y=41876$

Therefore, the best prediction for the population after 25 years is:

$\huge\boxed{\boxed{41,876}}$

Answer 2

Answer:

$C. \quad 41,876$

Step-by-step explanation:

The regression equation should have a variable raised to a power to represent the time. Assuming the correct equation is:

$y = 20,000 \times (1.03)^t$

where

• $t$ is the time in years,
• [tex} y [/tex] is the number of population.

Now, we want to find the population in year 25, so substitute $t = 25$ into the equation:

$y = 20,000 \times (1.03)^{25}$

Now, calculate this value to find the best prediction for the population in year 25.

$y \approx 20,000 \times (1.03)^{25}$

Using calculator:

$y \approx 20,000 \times 2.09377793$

$y \approx 41875.55859$

$y \approx 41876 \textsf{(in nearest whole number)}$

So, the correct option is:

$C. \quad 41,876$

Therefore, option C is the best prediction for the population in year 25 based on the given regression equation.