Question

The population (in millions) of the united states between 1970 and 2010 can be modeled as p(x) = 203.12e0.011x million people where x is the number of decades after 1970. the percentage of people in the united states who live in the midwest between 1970 and 2010 can be modeled as m(x) = 0.002x2 − 0.213x 27.84 percent where x is the number of decades since 1970.† how rapidly was the population of the midwest changing in 1980 and in 2000?

Answer 1

To find the rate at which the population of the Midwest was changing in 1980 and 2000, we need to calculate the derivative of the function representing the percentage of people in the Midwest.

Step-by-step explanation:

To find how rapidly the population of the Midwest was changing in 1980 and in 2000, we need to calculate the derivative of the function that models the percentage of people in the Midwest throughout the years.

The function that models the percentage of people in the Midwest is m(x) = 0.002x^2 - 0.213x + 27.84, where x is the number of decades since 1970.

Taking the derivative of this function will give us the rate of change, or the rate at which the population of the Midwest was changing.

So, let's find the derivatives of the function at x = 1 (1980) and x = 3 (2000):

m'(1) = 0.004 (the population's change rate in 1980)

m'(3) = -0.426 (the population's change rate in 2000)