I am given this data table:

Time After Consumption (min): 30, 60, 90, 120, 150, 180
Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5

Question:
I created a scatter plot of the data. Would y=3.5/30x+30.5 be an equation to model the amount of codeine in the bloodstream t minutes after taking the pill?

To determine if the equation y=3.5/30x+30.5 is a suitable model for the amount of codeine in the bloodstream at a given time, we need to compare the equation to the data points from the given table.

In the equation, y represents the amount of codeine in the bloodstream and x represents the time in minutes after consumption of the pill.

To verify if the equation accurately models the given data, we substitute each time value from the table into the equation and check if the corresponding value matches the data.

Let's substitute the given time values into the equation and compare the results:

For t = 30 minutes:
y = (3.5/30) * 30 + 30.5
y = 3.5 + 30.5
y = 34

For t = 60 minutes:
y = (3.5/30) * 60 + 30.5
y = 7 + 30.5
y = 37.5

For t = 90 minutes:
y = (3.5/30) * 90 + 30.5
y = 10.5 + 30.5
y = 41

For t = 120 minutes:
y = (3.5/30) * 120 + 30.5
y = 14 + 30.5
y = 44.5

For t = 150 minutes:
y = (3.5/30) * 150 + 30.5
y = 17.5 + 30.5
y = 48

For t = 180 minutes:
y = (3.5/30) * 180 + 30.5
y = 21 + 30.5
y = 51.5

Now, let's compare the calculated values to the given data points:

Given data:
Time After Consumption (min): 30, 60, 90, 120, 150, 180
Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5

By comparing the calculated values from the equation to the given data, we can observe that the values do not match accurately. Therefore, the equation y=3.5/30x+30.5 is not a suitable model to represent the amount of codeine in the bloodstream at a given time.

It's important to note that the given data may not necessarily follow a linear relationship, and it might require other mathematical models to accurately represent the relationship between time and the amount of codeine in the bloodstream.