SOLUTION: A biologist recorded a count of 320 bacteria present in a culture after 8 minutes and 1200 bacteria present after 26 minutes. Rounding to four decimal places, write an exponenti

Question 1129326: A biologist recorded a count of 320 bacteria present in a culture after 8 minutes and 1200 bacteria present after 26 minutes.
Rounding to four decimal places, write an exponential equation representing this situation.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
18 minutes between the two points

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Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

The general form of an exponential equation is

Given f(8)=320 and f(26)=1200, we have

Divide the 2nd equation by the first to eliminate a:

Use that value in either original equation to find the value of a:

= 177.84 to 2 decimal places.

We now have the a and b values for the exponential function.

ANSWER:

Check on a graphing calculator:
f(8) = 320.0033
f(26) = 1200.0124

The small error of course because of the rounding of the value of a.
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