Question 1. An environmental engineer has obtained a bacteria culture from a mun

Question

Question

1. An environmental engineer has obtained a bacteria culture from a municipal water sample and has allowed the bacteria to grow.

a) Show the resulting data and trendline, with equation and R2 value, on the appropriate graph type to make the data appear linear.

b) Assume the value of "m" in the resulting model is the growth constant. Use the trendline determined to find the value and units of the growth constant for this bacteria.

Question: For Part B, I got the equation, .y = 6.4196e0.3926x, for the graph when I plotted it. So would m=0.3926? Yes or No, and why?  I already know that there are no units for the growth constant.

*Please use Microsoft Excel and/or formulas to solve each part. Label each part accordingly.       

Explanation / Answer

The exponential model creates a trendline using the equation y = c * e bx

take the logarithm of both sides of the exponential formula it becomes

Ln(y) = Ln(c) + b * x and uses standard linear regression with Ln(y) as the dependent variable and x as the explanatory variable. That is, Excel finds the intercept and slope that minimize the sum of squared deviations between actual Ln(y) and predicted Ln(y), using the formula Ln(y) = Intercept + Slope * x

y = 6.4196e0.3926x

log(y) = log(6.4196) + 0.3926 * x

therefore m = 0.3926

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