Question

a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year:

I first found the derivative of f(t)=3e^-3t which is f'(t)=-9e^-3t. Then half a year would be 365/2 which is 182.5 days. When I substitute that in for t, i would get an answer of 0. What am i doing wrong?

Answer 1

Why are you using days when t was defined in years
so t = 1/2
f ' (1/2) = -9 e^(-3(1/2))
= -9 e^(-1.5)
= appr -2.008

Answer 2

Ah i see thanks!