Question

The population of a town can be modeled by the regression equation y = 18,000(1.04x). Which is the best prediction for the population in year 30?

Answer 1

Plugging in the year 30 would give y=18,000(1.04(30)) which would equal 561,000 as the population.

Answer 2

The approximated population of the town after 30 years will be 58382

Explanation:

The population of a town can be modeled by the regression equation :

`y=18000\cdot (1.04)^x`

where the initial population is 18000, y is the population of the town at any time x years

Now, we need to find the population of the town after 30 years.

So, Calculate the value of y by putting x = 30 in the given modeled equation.

`\implies y=18000\cdot (1.04)^x\\\\\implies y=18000\cdot (1.04)^(30)\\\\\implies y=18000* 3.24\\\\\implies y = 58381.16\\\\\implies y\approx 58382`

Hence, The approximated population of the town after 30 years will be 58382