SOLUTION: So lost can anyone help me? find k in the exponential function N(t)=N base0e^kt, given that N(0)=1 and N(3)=7. thanks in advance.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: So lost can anyone help me? find k in the exponential function N(t)=N base0e^kt, given that N(0)=1 and N(3)=7. thanks in advance.      Log On


   

Question 108088: So lost can anyone help me? find k in the exponential function
N(t)=N base0e^kt, given that N(0)=1 and N(3)=7. thanks in advance.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N%28t%29=N%5B0%5De%5Ekt where
N(0)=1 and N(3)=7
Use your two values to solve for k and N%5B0%5D
N%28t%29=1
N%280%29=1
N%5B0%5De%5E%28k%2A0%29=1
N%5B0%5D%2A1=1
N%5B0%5D=1
N%28t%29=N%5B0%5De%5Ekt
N%283%29=7
N%5B0%5De%5Ek%283%29=7
1%2Ae%5Ek%283%29=7
e%5Ek%283%29=7
k%283%29=ln%287%29
k=ln%287%29%2F3
k~0.649
Check your answers.
N%28t%29=e%5E0.649t
N%280%29=e%5E0.649%280%29
N%280%29=1
N%283%29=e%5E0.649%283%29
N%283%29=e%5E1.947
N%283%29=7.0
These values match your original values.
N%5B0%5D=1
k=ln%287%29%2F3