If N(t)=Ce^{-t}, where C is some constant, what is {dN(t)}/{dt}? Express your an

Question

If N(t)=Ce^{-t}, where C is some constant, what is {dN(t)}/{dt}?
Express your answer in terms of C, , and t.
{dN(t)}/{dt} =-Ce^(-t)    Correct


Part B
Given that at time t=0 there is a quantity of nuclei present N0 (in other words, N(0)=N0, find the value of the constant C in the equation N(t)=Ce^(-t).
Express your answer in terms of N0 and .
C =N0   Correct


Part C
Combining your answers from Parts A and B gives the equation N(t)=N0e^(- t). Find the time T1/2 at which half of the original number of nuclei will remain.
Express your answer in terms of N0 and .
T1/2 =(0.693)/    Correct

Part D
How many nuclei are left after a time 2T1/2?
Express your answer in terms of and N0
N =

Explanation / Answer

T1/2 = ln2 /

N(t)=N0e^(- t)

=> ln(No/N) = t

at t= 2 T1/2 = 2ln2 /

ln(No/N) = 2ln2 = ln4

=> N = No/4

one fourth are left after two half lifes

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