Find the half life of a substance which decays according to the function A (t) = 600e^-0.05t, where t is time in days. Round to the nearest day.

14 days

Step-by-step explanation:

The half life of a substance is the time required until the object has only half of the inicial mass.

So, to find the inicial mass of the object, we use t = 0 in the equation A (t):

A (0) = 600*e^0 = 600

Half of this mass is 300, so we can use A (t) = 300 and then find the time:

300 = 600e^-0.05t

e^-0.05t = 0.5

ln (e^-0.05t) = ln (0.5)

-0.05t = - 0.6931

t = 13.862 days

Rounding to nearest day, we have that t = 14 days