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?

Question

Responses
A 17.6917.69
B 18.7718.77
C 38.6938.69
D 42.3442.34
E 52.66

Answer 1

To find the concentration of the antibiotic after 3 hours, we need to substitute \( h = 3 \) into the function \( C(h) = -0.09h^2 + 3.5h + 8 \).

Let's do the calculation step by step:

1. Substitute \( h = 3 \) into the equation: \[ C(3) = -0.09(3^2) + 3.5(3) + 8 \]

2. Calculate \( 3^2 \): \[ 3^2 = 9 \]

3. Now substitute back into the equation: \[ C(3) = -0.09(9) + 3.5(3) + 8 \]

4. Calculate \( -0.09(9) \): \[ -0.09 \times 9 = -0.81 \]

5. Calculate \( 3.5(3) \): \[ 3.5 \times 3 = 10.5 \]

6. Now add all the calculated values: \[ C(3) = -0.81 + 10.5 + 8 \] \[ C(3) = -0.81 + 18.5 \] \[ C(3) = 17.69 \]

So the concentration of the antibiotic after 3 hours is \( 17.69 \) parts per million, rounded to the nearest hundredths.

The correct response is: A 17.69