The amount of medicine in micrograms, A, in a person's bloodstream t minutes after a certain quantity of it has been inhaled can be approximated by the equation Upper A equals negative 40 t squared plus 160 t. How long after inhalation will there be about 120 micrograms of medicine in the bloodstream?

After 1 second and after 3 seconds.

Explanation:

the amount of medicine in time t is given by A = -40t2 + 160t.

To know the time when the amount of medicine will be 120 micrograms, we need to make the expression A equals 120, and then find the value of t:

120 = -40t2 + 160t

-40t2 + 160t - 120 = 0

dividing everything by -40, we have

t2 - 4t + 3 = 0

we have a second order equation, and to find its roots, we can use the baskhara formula:

D = b2 -4ac = 16 - 12 = 4.

The square root of D is +2 or -2

t_1 = (4 + 2)/2 = 3

t_2 = (4 - 2)/2 = 1

We have two values of t, both acceptable. So, after 1 second and after 3 seconds of the inhalation, there will be 120 micrograms of medicine in the bloodstream.