SOLUTION: The values of y, y0, and t are given. For an equation of the form y=y0e^kt, give the exact value of k in terms of natural logarithms. y0=70, t=110, y=35 k=?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The values of y, y0, and t are given. For an equation of the form y=y0e^kt, give the exact value of k in terms of natural logarithms. y0=70, t=110, y=35 k=?      Log On


   

Question 1076016: The values of y, y0, and t are given. For an equation of the form y=y0e^kt, give the exact value of k in terms of natural logarithms.
y0=70, t=110, y=35
k=?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=y%5B0%5De%5E%28kt%29 , give the exact value of k in terms of natural logarithms
y%5B0%5D=70,
t=110,
y=35
k=?

35=70e%5E%28k%2A110%29

35%2F70=e%5E%28110k%29

1%2F2=e%5E%28110k%29 .........take natural logarithms

ln%281%2F2%29=ln%28e%5E%28110k%29%29

ln%281%29-ln%282%29=%28110k%29ln%28e%29........since ln%28e%29=1 and ln%281%29=0, we have

-ln%282%29=110k

k=-ln%282%29%2F110