SOLUTION: In a Microbiology class laboratory experiment the following data was obtained using certain bacteria in the incubator in a specified environment. Time in Hours: 0 | 1 | 2 | 3 |

Algebra ->  Exponents -> SOLUTION: In a Microbiology class laboratory experiment the following data was obtained using certain bacteria in the incubator in a specified environment. Time in Hours: 0 | 1 | 2 | 3 |       Log On


   

Question 1103928: In a Microbiology class laboratory experiment the following data was obtained using certain bacteria in the incubator in a specified environment.
Time in Hours: 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Number of Bacteria: 500 | 645 | 825 | 1060 | 1360 | 1750 | 2250 | 2890
Find the equation for the exponential model corresponding to the data. Find R for the model.
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
Time in Hours:        0 |  1  |  2  |  3   |   4  |   5  |  6   |  7  |

Number of Bacteria: 500 | 645 | 825 | 1060 | 1360 | 1750 | 2250 | 2890  , call each Y

log base 10 of Y:  2.70 | 2.81| 2.92| 3.03 | 3.13 | 3.24 | 3.35 | 3.46

Difference            0.11   0.11  0.11  0.10   0.11   0.11    0.11

Notice that the differences in log base 10 for Y are nearly all the same, 0.11. This means log%2810%2CY%29 is a linear function of time x in hours. You could choose as a vertical axis intercept, (0, 2.70). The goal is to finally get an exponential function but you can start with the linear form of it.

log%28%28Y%29%29=0.11x%2B2.70, continue from here.
(Or better, log%28%28Y%29%29=0.11x%2Blog%28%28500%29%29 ).

You can get highlight%28Y=500%2A10%5E%280.11x%29%29

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You could choose base other than 10 and find something similar.