Question

The concentration, in parts per million, of a type of antibiotic in a human's bloodstream after h hours can be modeled by the polynomial function C(h) = −0.09h2 + 3.5h + 8. What is the concentration of the antibiotic after 3 hours in parts per million to the nearest hundredths?

Answer 1

`C(3)=17.69\ ppm`

Explanation:

Given:

Given polynomial function is.

`C(h)=-0.09h^(2) +3.5h+8`

Hours
`h=3`

We need to find the concentration of the antibiotic after 3 hours.

Solution:

Rewrite the given polynomial function as.

`C(h)=-0.09h^(2) +3.5h+8`

Substitute
`h=3` in given polynomial function.

`C(3)=-0.09(3)^(2) +3.5* 3+8`

`C(3)=-0.09* 9+10.5+8`

`C(3)=-0.81+10.5+8`

`C(3)=-0.81+18.5`

`C(3)=17.69\ ppm`

Therefore, the concentration of the antibiotic after 3 hours
`C(3)=17.69\ ppm` .