SOLUTION: An experiment began with 200 of a certain type of bacteria. The bacteria grew exponentially, and 4 hours later there were 18,000. 1. Fit an exponential model to these data.

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Question 867280: An experiment began with 200 of a certain type of bacteria. The bacteria grew exponentially, and 4 hours later there were 18,000.

1. Fit an exponential model to these data.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You expect a general formula P=p%2Ae%5E%28kt%29, where P is population count after any time t; t is time in hours, p is initial population, and k is a constant characterizing the conditions and this bacteria.

You need to know a value for k.
ln%28P%29=ln%28p%29%2Bkt
kt=ln%28P%29-ln%28p%29
kt=ln%28P%2Fp%29
k=%281%2Ft%29ln%28P%2Fp%29
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Your description gives p=200, P=18000, and t=4. Use these values to compute k.
Result is highlight_green%28k=1.125%29
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Fit a more specific model, you might want to keep the same value for p, and now include the k value:
highlight%28P=200e%5E%281.125t%29%29