Question

1. the amount of medicine in elizabeth’s blood is modeled by the function $m(t) = -t^2 + 10t$, where $t$ is the number of hours after she takes the medicine. how many hours after elizabeth takes her medicine is the amount of medicine in her blood the highest?

a 5 hours
b 10 hours
c 25 hours

Explanation:

Step1: Identify quadratic form

The function $M(t) = -t^2 + 10t$ is a quadratic function in the form $at^2 + bt + c$, where $a=-1$, $b=10$, $c=0$.

Step2: Find vertex t-value

For a quadratic $at^2+bt+c$, the vertex (maximum, since $a<0$) occurs at $t = -\frac{b}{2a}$.
Substitute values: $t = -\frac{10}{2(-1)}$

Step3: Calculate the result

Simplify the expression: $t = \frac{-10}{-2} = 5$

Answer:

A. 5 hours