Question 375947: Determine the constants N(o) and K so that the graph y=N(o)e^(kt) passes through the points (2,3) and (8,24).
I dont even know how to start this problem... any help would be greatly appreciated!!
Found 2 solutions by robertb, user_dude2008:
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! From the given point (2,3),  .
From the given point (8,24),  .
Raise the 1st equation to the 4th power, to get  , or  .
Divide this resulting equation by , to get  , resulting in  .
Hence  , or  , or  .
Answer by user_dude2008(1862)  (Show Source):
You can put this solution on YOUR website! y=N(o)e^(kt)
3=N(o)e^(2k)
N(o)=3/e^(2k)
y=N(o)e^(kt)
24=(3/e^(2k))e^(8k)
24=3e^(6k)
8=e^(6k)
6k=ln(8)
k=ln(8)/6
k=3ln(2)/6
k=ln(2)/2
N(o)=3/e^(2k)
N(o)=3/e^(2*ln(2)/2)
N(o)=3/e^(ln(2))
N(o)=3/2
Answer: equation is y = 3/2 e^(ln(2)/2 t)
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