Chapter 9.6, Problem 50PPS

(a)

To determine

Complete the table

Answer to Problem 50PPS

Time (hour)	Number of Bacteria   $2^x$
0	1
1	2
2	4
3	8
4	16
5	32
6	64

Explanation of Solution

Given:

The table

  

Concept Used:

  $2^x$

Calculation:

In order to find the table we put the values of x in $2^x$ and simplify further as shown below:

  $\begin{array}{c}Atx=0\\ n=2^x=2^0\\ =1\\ Atx=1\\ n=2^x=2^1\\ =2\\ Atx=2\\ n=2^x=2^2\\ =4\\ Atx=3\\ n=2^x=2^3\\ =8\\ Atx=4\\ n=2^x=2^4\\ =16\\ Atx=5\\ n=2^x=2^5\\ =32\\ Atx=6\\ n=2^x=2^6\\ =64\end{array}$

Time (hour)	Number of Bacteria   $2^x$
0	1
1	2
2	4
3	8
4	16
5	32
6	64

(b)

To determine

The graph from the table

Answer to Problem 50PPS

  

Explanation of Solution

Given:

The table

Time (hour)x	Number of Bacteria y= $2^x$
0	1
1	2
2	4
3	8
4	16
5	32
6	64

Concept Used:

In rectangular coordinate system any point be in the form of $\left(x,y\right)$ .

• In Quadrant I, both the coordinates of ordered pair are positive, that is, $\left(+,+\right)$ .
• In Quadrant II, first number is negative and second is positive, that is, $\left(-,+\right)$ .
• In Quadrant III, both the coordinates of ordered pair are negative, that is, $\left(-,-\right)$ .
• In Quadrant IV, first point is positive and second is negative, that is, $\left(+,-\right)$ .

In order to plot the points $\left(0,1\right),\left(1,2\right),\left(2,4\right),\left(3,8\right),\left(4,16\right),\left(5,32\right),\text{and}\left(6,64\right)$

, observe that they all numbers are same they are positive, so the point will be in first quadrant.The graph of the point is shown below:

  

(c)

To determine

The number of bacteria after every hour and function models the pattern in the table

Answer to Problem 50PPS

The number of bacteria is double to the previous one.

The function that models the pattern in the table is $y=2^x$

Explanation of Solution

Given:

The table

We see that in every hour the number of bacteria is double to the previous one.

The function that models the pattern in the table is $y=2^x$