Question

The percentage of obese children aged 12-19 years in the United States is approximatelyP(t) = 0.04t + 4.6 if 0 ≤ t < 10−0.01005t2 + 0.945t − 3.4 if 10 ≤ t ≤ 30where t is measured in years, with t = 0 corresponding to the beginning of 1970. What was the percentage of obese children aged 12-19 at the beginning of 1975? At the beginning of 1986? At the beginning of 1995? (Round your answers to two decimal places.)

Answer 1

4.8% of of obese children aged 12-19 at the beginning of 1975.

9.15% of obese children aged 12-19 at the beggining of 1986

13.94% of obese children aged 12-19 at the beggining of 1995

Explanation:

The percentage of obese children aged 12-19 years in the United States is given by the following piecewise function:

`P(t) = \left \{ {{0.04t + 4.6, 0 \leq t < 10}\atop {-0.01005t^(2) + 0.945t - 3.4, 10 \leq t < 30}} \right.`

In which t is measured in years.

What was the percentage of obese children aged 12-19 at the beginning of 1975?

This is the value of P when t = 5, so
`P(5)`.

For P(5), we apply the first definition of the piecewise function.

`P(5) = 0.04(5) + 4.6 = 0.2 + 4.6 = 4.8`

At the beginning of 1986?

The value of P when t = 16, so
`P(16)`.

For P(16), we apply the second definition of the piecewise function.

`P(16) = -0.01005(16)^(2) + 0.945(16) - 3.4 = 9.15`

At the beginning of 1995?

The value of P when t = 25, so
`P(25)`.]

For P(25), we apply the second definition of the piecewise function.

`P(16) = -0.01005(25)^(2) + 0.945(25) - 3.4 = 13.94`