Question

The amount of medicine in Elizabeth block is modeled by the function m(t)=-t² + 20t where t is in the number of hours. Determine how many hours after Elizabeth takes the medicine is it in his blood highest?

Answer 1

The amount of medicine in Elizabeth's blood is modeled by a quadratic function. The medicine is at its highest concentration 10 hours after she takes it.

Step-by-step explanation:

The amount of medicine in Elizabeth's blood is modeled by the function m(t) = -t² + 20t, where t is the number of hours. To determine when the medicine is at its highest concentration, we need to find the maximum value of the function.

To find the maximum value of a quadratic function, we can use the formula t = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -1 and b = 20, so we have t = -20/(2*(-1)) = 10.

Therefore, the medicine is at its highest concentration in Elizabeth's blood 10 hours after she takes it.