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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
18 minutes between the two points

320%2Ab%5E18=1200

b%5E18=3.75

log%28%28b%29%29%2A18=3.75

log%28%28b%29%29=0.20833

b=1.616

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y=p%2A1.616%5Ex
p%2A1.616%5E8=320
p=6.880
highlight_green%28y=6.880%2A1.616%5Ex%29

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


The general form of an exponential equation is

f%28x%29+=+ab%5Ex

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

ab%5E8=320
ab%5E26=1200

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

b%5E18+=+1200%2F320+=+15%2F4+=+3.75
b+=+3.75%5E%281%2F18%29

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

a%283.75%29%5E%288%2F18%29+=+320
a+=+320%2F%28%283.75%5E%288%2F18%29%29%29 = 177.84 to 2 decimal places.

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

ANSWER: f%28x%29+=+177.84%283.75%5E%28x%2F18%29%29

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.