the neutral exponential function

Question

Radioactive Decay A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function

m(t)= 13e^-0.015t

where m(t) is measured in kilograms. (a) Findthemassattimet t=0.

(b) How much of the mass remains after 45 days?

Answer 1

First, insert spaces where needed in (a) so you can "Find the mass at time t t=0." Now use t = 0 days to give you 13 kg of mass at outset (because exp0 = 1).

 

plug in t=45 days to get

 

m(45 d) = 13*exp(-0.015/d*45 d) = 13*exp(-0.675) = 6.62 kg.

 

Finally, remove the spaces you added at outset, and you have

 

Findthemassattimet t=0 = 6.62 kg.

Answer 2

a) plug in zero for t.  m(t)=13e⁰ = 13 kg

 

b) plug in 45 for t  m(t)= 6.62 kg