Rearrange the following equation?

Question

N=N◦ eˉλt

the equations hard to write on a computer, its basically... N equals N with a little o down next to it. e to the power of minus lamda t

thanks

make t the subject

Answer 1

N = No e^(- λ t)
N / No = e^(- λ t)
N / No = 1 / e^( λ t)
e^(λ t) = No / N
(λ t) = ln (No / N)
t = (1/ λ ) ln (No / N)

Answer 2

What argument would you like it resolved for?

for t or lambda, observe that by dividing both sides with N_o, you get

e^(-lambda t) = N/N_o

take the natural logarithm on both sides:

-lambda t = ln (N/N_o)

Your answer is one of the following:

t= -1/lambda * ln (N/N_o)
lambda= -1/t * ln (N/N_o)