A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function
m(t) = 9e−0.012t
where m(t) is measured in kilograms.
(a) Find the mass at time t = 0.
I am sure you meant:
m(t) = 9 e^(-.012t)
so if t = 0 , remember that anything^0 = 1
so m(0) = 9
well, I suppose I will try although really I am sure you could try first.
9 e^-(.012*49)
= 9/(e^.588)
= 9/1.8
= 5
ALSO How much of the mass remains after 49 days? (Round your answer to one decimal place.) what would this look like just to double check?
To find the mass at time t = 0, we can substitute t = 0 into the function m(t) = 9e^(-0.012t).
m(0) = 9e^(-0.012 * 0)
Since anything raised to the power of zero equals 1, we have:
m(0) = 9e^(0)
e^(0) is equal to 1, so we further simplify:
m(0) = 9 * 1
m(0) = 9
Therefore, the mass at time t = 0 is 9 kilograms.