Question

The number of milligrams of a diabetic drug in a person's system after t hours is given by the function D(t)=20e^(-0.4t). Use the function to determine when the drug level will reach 0.01 mg (round to nearest hour).

Answer 1

@jim_thompson5910

Answer 2

Now plug in D(t) = 0.01 and solve for t


D(t)=20e^(-0.4t)


0.01 = 20e^(-0.4t)


0.01/20 = e^(-0.4t)


0.0005 = e^(-0.4t)


ln(0.0005) = -0.4t


-7.600902 = -0.4t


-7.600902/(-0.4) = t


19.002255 = t


t = 19.002255


Which rounds to 19. So it will take about 19 hours for the drug level to reach 0.01 mg

Answer 3

I really appreciate you taking time to walk me through these, thank you so much! =)

Answer 4

anytime