Consider the following: A medical researcher wants to determine the effects of pH (a measure of alkalinity or acidity, with pure water having a pH of 7) on the growth of a bacteria culture. The data provided to you below represents the measurements of different cultures (in the thousands of bacteria) after 8 hours.

See below

Step-by-step explanation:

Data in the table:

PH             4       5     6     7     8    9     10     11

Bacteria    116   120  131  136  141  151  148   163

See attached for scatter plot

We can see the chart is close to linear function. Let's build one based on data in the table

The line will be in the form of:

If we use two points and get the equation

Finding the slope:

Then, finding y-intercept:

So the line is:

Note: This is approximate best fit graph and it is attached as well. Exact formula for the line is built by using different method and is very close to the one above

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x