   Chapter 2.5, Problem 12TE

Chapter
Section
Textbook Problem

OBESE Children in the United States The percentage of obese children aged 12-19 in the United States is approximately P ( t ) = { 0.04 t + 4.6 if  0 ≤ t < 10 − 0.01005 t 2 + 0.945 t − 3.4 if 1 0 ≤ t ≤ 30 where t is measured in years, with t = 0 corresponding to the beginning of 1970.Plot the graph of P(t).What was the percentage of obese children aged 12-19 at the beginning of 1970? At the beginning of 1985? At the beginning of 2000?Source: Centers for Disease Control and Prevention.

(a)

To determine

To sketch: The graph of the function P(t) .

Explanation

In United States, the percentage of Obese children aged 1219years is,

P(t)={0.04t+4.6if0t<100.01005t2+0.945t3.4if10t30 (1)

Where t is measured in years, with t=0 corresponding to the beginning of 1970 .

Graph:

Substitute the values of t to find the value of the percentage of the Obese children.

Substitute 0 for t in equation (1) to find the value of P(t) ,

P(0)=0.04(0)+4.6=4.6

Substitute 5 for t in equation (1) to find the value of P(t) ,

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

Substitute 10 for t in equation (1) to find the value of P(t) ,

P(10)=0.01005(10)2+0.945(10)3.4=1.005+9.453.4=5.045

Substitute 15 for t in equation (1) to find the value of P(t) ,

P(15)=0.01005(15)2+0.945(15)3.4=2.26+14.1753.4=8.515

Substitute 20 for t in equation (1) to find the value of P(t) ,

P(20)=0

(b)

To determine
The percentage of Obese children aged 1219 at the beginning of 1970,1985and2000 .

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