Question

A sample initially contains 200 grams of a certain radioactive isotope. After 5 hours, the amount has decayed to 177 grams. Let A(t) denote the amount (in grams) of the isotope after t hours. Assume that

A ( t ) = C e ^( k t )

for some constants C and k.

Find C

Answer 1

We are given

Since, A sample initially contains 200 grams of a certain radioactive isotope

so,

A(t)=177 when t=5

we can plug values into formula

now, we can solve for k

now, we can plug it back

and we get

..........Answer