Question 375947
From the given point (2,3), {{{3 = N(0)e^(2k)}}}.  

From the given point (8,24), {{{24 = N(0)e^(8k)}}}. 

Raise the 1st equation to the 4th power, to get {{{3^4 = (N(0))^4*e^(8k)}}}, or {{{81 = (N(0))^4*e^(8k)}}}. 

Divide this resulting equation by {{{24 = N(0)e^(8k)}}}, to get {{{81/24 = 27/8 = (N(0))^3}}}, resulting in {{{N(0) = 3/2}}}.  

Hence {{{3 = (3/2)*e^(2k)}}}, or {{{2 = e^(2k)}}}, or {{{k = ln2/2}}}.