m = Ce−kt
Now we can solve for C by plugging in m = 10,000 and t = 0:10,000 = Ce^0 , so C = 10,000.
This gives us the equation m = 10,000e−kt. Next, we can solve for k by plugging in m = 5,000
and t = 5,750.
5,000 = 10,000e−5,750k
= e−5,750k
Therefore, the equation for the mass m of the element at time t is m ≈ 10,000e−.000121t, or if we
want an exact solution, it is m = 10,000.
Finally, we can solve for the mass of the element at time t = 1,000: m ≈ 10,000e−.000121(1,000) ≈
8,860 gms or m = 10,000 ≈ 8,864 gms. (And, if we are concerned with significant
figures, the mass can be written as 8,900.)
9.
