A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :
| x (time in hours) | 0 | 4 | 8 | 12 | 16 | 20 | 24 |
| y | 25 | 36 | 52 | 68 | 85 | 104 | 142 |
We are asked to fit the population data to an exponential model (y = \alpha e^{\beta x}). To do this numerically by hand, we can linearize the model using logarithms. Take the natural logarithm on both sides: [ \ln y = \ln \alpha + \beta x ] Let (Y = \ln y) and (A = \ln \alpha). Then the equation becomes linear: [ Y = A + \beta x ] --- Step 1: Compute (\ln y) values | x (h) | y | ln y | | ________ ____ _______ ___ ______ __________ _____.
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