Question

The most significant time to be aware of the UV index on a sunny day is modelled by the function f(x) = -0.08(x-13)2 + 9 where x is the time of day on a 24-hour clock and f(x) represents the UV index. What is the UV index at 2 pm? When will the UV index be 7?

Answer 1

`\begin{gathered} f(x)=\text{ -}0.08(x\text{ -13\rparen}^2+9 \\ \\ 2pm\text{ }or\text{ 14h} \\ f(14)=\text{ -}0.08(14\text{ -}13)^2+9 \\ f(14)=\text{ -}0.08(1^2)+9 \\ f(14)=\text{ -}0.08(1)+9 \\ f(2)=8.92 \\ \\ f(x)=\text{ 7 \lparen when will UV index be 7?\rparen} \\ 7=\text{ -0.08}(x\text{ -}13)^2+9 \\ 7\text{ - }9=\text{ -0.08\lparen}x\text{ -}13^{\text{ }})^2 \\ \frac{\text{ -}2}{\text{ -}0.08}=(x\text{ - }13)^2\text{ } \\ 25=(x\text{ - }13)^2 \\ √(25)=\sqrt{(x\text{ -}13)^2} \\ 5=x\text{ - 13} \\ x=13+5 \\ x=18\text{ \lparen6pm\rparen} \end{gathered}`

The UV index at 2 pm will be 8.92, and it will be 7 at 6 pm