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

The concentration in parts per million of a type of antibiotic given by a polynomial function,

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

Where, h = number of hours.

We have to find C(h) when h = 3.

We will have to plug in h = 3 in the given polynomial function. We will get,

$C(h) = -0.09(3)^2+3.5(3)+8$

$C(h) = -0.09(9)+(3.5)(3)+8$

$C(h) = -0.81+(3.5)(3)+8$

$C(h) = -0.81+10.5+8$

$C(h) = -0.81+18.5$

$C(h) = 17.69$

So we have got the required concentration.

The required concentration is 17.69.

Answer 2

C(h) = −0.09h^2 + 3.5h + 8
sub in 3 for H
C(3) = -0.09(3)^2 + 3.5 (3) + 8
=17.69 ppm
Hope that helps! :)