Question

question 1 - 15
a study shows that hospital admissions for asthma, a breathing disorder, increase on days when the concentration of ozone in the air is elevated. surprisingly, low concentrations of ozone actually decrease asthma admissions. this is because another chemical released with the ozone has beneficial effects, although these are overcome by the negative effects of higher ozone concentrations. the graph shows that hospital asthma admissions as a function of ozone concentration fit a parabolic model:
( y = 0.01x^{2}-0.6x + 19.5 ).
what are the coordinates at which asthma admissions are at the same level as when there are no ozone emissions at all?
( (30,10.5) )
( (100,10.5) )
( (20.1,1.5) )
( (60,19.5) )

Explanation:

Step1: Find the value of \(y\) when \(x = 0\)

Substitute \(x = 0\) into the equation \(y=0.01x^{2}-0.6x + 19.5\)

$$
LATEXBLOCK0
$$

Step2: Substitute \(y = 19.5\) into the equation and solve for \(x\)

Set \(y = 19.5\) in \(y=0.01x^{2}-0.6x + 19.5\)

$$
LATEXBLOCK1
$$

One solution is \(x = 0\). For \(0.01x-0.6=0\), we have \(0.01x=0.6\), so \(x = 60\)

Answer:

\((60,19.5)\)