Question

Plz help (URGENT) The data shows the number of bacteria in a culture after a given number of hours. Based on the data, which is closest to the number of hours it takes the culture to reach 12,000 bacteria? A) 16 hours B) 19 hours C) 22 hours D) 25 hours Hour Bacteria 1 2,215 2 2,235 3 2,360 4 2,680 5 3,075

Answer 1

Answer:

The number of hours it takes the culture to reach 12,000 bacteria is 41 hours.

Step-by-step explanation:

To predict the number of hours it takes to culture a certain number of bacteria form a regression equation of number of hours (y) based on the number of bacteria (x) using the provided data.

The general form of the regression equation is:

$y=a+bx$

Compute the values of a and b as follows:

$a=\frac{\sum Y\cdot\sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{15\cdot 32109075 - 12565\cdot 39860}{5\cdot 32109075-(12565)^{2}}=-7.203\\\\b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{5\cdot 39860- 12565\cdot 15}{5\cdot 32109075-(12565)^{2}}=0.004$

*Use the Excel data sheet attached.

The regression equation of number of hours based on the number of bacteria is:

$y=-7.203+0.004x$

Compute the number of hours it takes the culture to reach 12,000 bacteria as follows:

$y=-7.203+0.004x$

   $=-7.203+(0.004\times 12000)\\=-7.203+48\\=40.797\\\approx 41$

Thus, the number of hours it takes the culture to reach 12,000 bacteria is 41 hours.