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?
Accepted Solution
A:
Answer:[tex]C(3)=17.69\ ppm[/tex]Step-by-step explanation:Given:Given polynomial function is.[tex]C(h)=-0.09h^{2} +3.5h+8[/tex]Hours [tex]h=3[/tex]We need to find the concentration of the antibiotic after 3 hours.Solution:Rewrite the given polynomial function as.[tex]C(h)=-0.09h^{2} +3.5h+8[/tex]Substitute [tex]h=3[/tex] in given polynomial function.[tex]C(3)=-0.09(3)^{2} +3.5\times 3+8[/tex][tex]C(3)=-0.09\times 9+10.5+8[/tex][tex]C(3)=-0.81+10.5+8[/tex][tex]C(3)=-0.81+18.5[/tex][tex]C(3)=17.69\ ppm[/tex]Therefore, the concentration of the antibiotic after 3 hours [tex]C(3)=17.69\ ppm[/tex] .