Math  Exponential
posted by Anonymous on .
Please check my answers and methods if they are correct! Thanks in advance.
Suppose the % of alc. in the blood, t, hours after consumption is C(t) = 0.3te^(t/2). How much time passes before the blood alcohol lvl starts to decrease?
C'(t) = 0.3e^(t/2)  0.15te^(t/2)
C'(t) = e^(t/2)(0.3  0.15t)
0 = 0.3  0.15t
t = 2 hours
So... 2 hours passes before it starts to decrease

Records show that, t, weeks after the outbreak of a specific disease, approx. Q(t) = 15/(1 + 14e^(1.7t)) thousand people had caught it. If the trend continues, approx. how many people will eventually contract it?
Q(0) = 15/1
Q(0)  15 000
So... 15,000 people will contract the disease.

I agree with both of your answers