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 of bacteria present after 16 hours, to the nearest whole number.

hours (x)

0

1

2

3

4

5

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bacteria (y)

940

1034

1105

1223

1352

1520

copy values for calculatoropen statistics calculatoranswerregression equation:final answer:

Explanation:

Step1: Recall exponential regression form

The general exponential regression equation is $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor.

Step2: Calculate regression coefficients

Using a statistics calculator with the given data:
$x = [0,1,2,3,4,5]$, $y = [940,1034,1105,1223,1352,1520]$
We find $a \approx 939.99$ and $b \approx 1.09$ (rounded to nearest hundredth).
So the equation is $y = 939.99(1.09)^x$.

Step3: Substitute x=16 into the equation

$$y = 939.99(1.09)^{16}$$
First calculate $1.09^{16} \approx 3.97030588$
Then $y \approx 939.99 \times 3.97030588$

Step4: Compute the final value

$y \approx 939.99 \times 3.97030588 \approx 3732$

Answer:

Regression Equation:

$y = 939.99(1.09)^x$

Final Answer:

3732