Question

PLEASEEEE HELPPPP

The amount of medicine in Elizabeth's blood is modeled by the
function
M(t) = -t² + 5t,
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?

Answer 1

Answer:
The amount of medicine in Elizabeth's blood is the highest at t = 2.5 hours.

Work:

To find the time when the amount of medicine in Elizabeth's blood is the highest, we need to find the maximum value of the function M(t) = -t² + 5t.

We know that the maximum value of a quadratic function occurs at its vertex. The x-coordinate of the vertex of a quadratic function in the form of ax² + bx + c is given by -b/2a.

In this case, a = -1 and b = 5, so the x-coordinate of the vertex is -b/2a = -5 / 2(-1) = 2.5.

Therefore, the amount of medicine in Elizabeth's blood is the highest at t = 2.5 hours.