SOLUTION: I wasn't quite sure where to put this question, so I'm asking it here: The number of rabbits increased exponentially. At first there were 400. Three years later there were 1600. Ho

Algebra ->  Probability-and-statistics -> SOLUTION: I wasn't quite sure where to put this question, so I'm asking it here: The number of rabbits increased exponentially. At first there were 400. Three years later there were 1600. Ho      Log On


   

Question 1100702: I wasn't quite sure where to put this question, so I'm asking it here: The number of rabbits increased exponentially. At first there were 400. Three years later there were 1600. How many rabbits would there be at the end of 10 years? My answer was 41000, but the answer book's answer was 40,637. I can't find where I went wrong. Can you help me? Thank you so much for your time!
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
r=p%2Ae%5E%28kx%29 , not sure this the best model to pick


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number of rabbits increased exponentially. At first there were 400. Three years later there were 1600.
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1600=400%2Ae%5E%28k%2A3%29
e%5E%283k%29=4
ln%28e%5E%283k%29%29=ln%284%29
3k%2A1=ln%284%29
k=ln%284%29%2F3
k=0.4621
highlight_green%28r=400%2Ae%5E%280.4621x%29%29
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Now, how much is r, when x is 10 years?
r=400%2Ae%5E%280.4621%2A10%29
r=400%2Ae%5E%284.621%29
r=400%2A101.60
highlight%28r=40640%29
If you wanted to round to the nearest hundred, you could, and it would be 41000; or you might round to nearest tens, and r is 40600.



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ALTERNATIVE
Population is multiplied by 4, every three years.
y=400%2AR%5Ex
1600=400%2AR%5E3
4=R%5E3
log%2810%2C4%29=3%2Alog%2810%2CR%29
%281%2F3%29%2Alog%2810%2C4%29=log%2810%2CR%29
log%2810%2C%284%5E%281%2F3%29%29%29=log%2810%2CR%29
R=4%5E%281%2F3%29
R=1.5874
MODEL: highlight_green%28y=400%2A1.5874%5Ex%29
When x=10?
y=400%2A1.5874%5E10
y=400%2A1.01593
highlight_green%28y=40637%29, and you could round this to whatever accuracy you want.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a simplification of the "alternative" method shown by the other tutor....

The population increases by a factor of 4 every 3 years.

So the population after 10 years will be the original population, multiplied by 4 (10/3) times:
400%284%5E%2810%2F3%29%29+=+40673 to the nearest whole number.