Question

The accompanying table shows the number of bacteria present in a certain culture

over a 5 hour period, where x is the time, in hours, and y is the number of

bacteria. Write an exponential regression equation for this set of data, rounding all

coefficients to the nearest hundredth. Using this equation, determine the number o

bacteria present after 13 hours, to the nearest whole number.

Hours (x) Bacteria (y)

0 1892

1

2106

2

2

2342

3

2525

4

2819

4

5

5

3042

Answer 1

The general form of the exponential regression equation that models the number of bacteria  is y = ab^x

The exponential regression equation is y = 1910.38 * 1.1^x

How to determine the exponential regression equation?

The dataset is given as:

x     y

0    1892

1     2106

2    2342

3    2525

4    2819

5    3042

To determine the exponential regression equation, we make use of a graphing calculator.

From the graphing calculator, we have the following calculation summary

a = 1910.38

b = 1.10

An exponential regression equation is represented as:

y = ab^x

So, we have:

y = 1910.38 * 1.1^x

Hence, the exponential regression equation is y = 1910.38 * 1.1^x

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