Question

the number of births in a particular city is modeled by B(x)=-2.8x^2+17x+5102 and the number of deaths by D(x)=3.3x^2-12x+2350 where x is years after 2012. What is the function modeling the chnage in population each year

Answer 1

The function modeling the change in population each year would be the difference between the number of births (B(x)) and the number of deaths (D(x)). So, the change in population function (C(x)) can be expressed as:

C(x) = B(x) - D(x)

Given B(x) = -2.8x^2 + 17x + 5102 and D(x) = 3.3x^2 - 12x + 2350, you can subtract D(x) from B(x) to get the change in population:

C(x) = (-2.8x^2 + 17x + 5102) - (3.3x^2 - 12x + 2350)

Now, let's simplify the expression:

C(x) = -2.8x^2 + 17x + 5102 - 3.3x^2 + 12x - 2350

Combine like terms:

C(x) = (-2.8x^2 - 3.3x^2) + (17x + 12x) + (5102 - 2350)

C(x) = -6.1x^2 + 29x + 2752

So, the function modeling the change in population each year is:

C(x) = -6.1x^2 + 29x + 2752

This function represents how the population changes each year, taking into account both births and deaths as a function of years (x) after 2012.

Answer 2

So, the function modeling the change in population each year is:

C(x) = -6.1x^2 + 29x + 2752

Explanation:

To find the function modeling the change in population each year, you can subtract the number of deaths (D(x)) from the number of births (B(x)). The change in population (C(x)) is given by:

C(x) = B(x) - D(x)

So, let's subtract D(x) from B(x):

C(x) = (-2.8x^2 + 17x + 5102) - (3.3x^2 - 12x + 2350)

Now, let's simplify the expression:

C(x) = -2.8x^2 + 17x + 5102 - 3.3x^2 + 12x - 2350

Combine like terms:

C(x) = (-2.8x^2 - 3.3x^2) + (17x + 12x) + (5102 - 2350)

C(x) = -6.1x^2 + 29x + 2752

So, the function modeling the change in population each year is:

C(x) = -6.1x^2 + 29x + 2752

This function represents the net change in population each year, taking into account both births and deaths.