Respuesta :
Answer:
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
Step-by-step explanation:
The percentage of obese children aged 12-19 years in the United States is given by the following piecewise function:
[tex]P(t) = \left \{ {{0.04t + 4.6, 0 \leq t < 10}\atop {-0.01005t^{2} + 0.945t - 3.4, 10 \leq t < 30}} \right.[/tex]
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 [tex]P(5)[/tex].
For P(5), we apply the first definition of the piecewise function.
[tex]P(5) = 0.04(5) + 4.6 = 0.2 + 4.6 = 4.8[/tex]
At the beginning of 1986?
The value of P when t = 16, so [tex]P(16)[/tex].
For P(16), we apply the second definition of the piecewise function.
[tex]P(16) = -0.01005(16)^{2} + 0.945(16) - 3.4 = 9.15[/tex]
At the beginning of 1995?
The value of P when t = 25, so [tex]P(25)[/tex].]
For P(25), we apply the second definition of the piecewise function.
[tex]P(16) = -0.01005(25)^{2} + 0.945(25) - 3.4 = 13.94[/tex]
