Part 1:
A patient is given a 250 mg dose of a certain medication. Their body filters (that is, removes) 15% of whatever amount of the drug is left in the body each hour. 1. a) Start by filling out the table below. You can round each amount to the nearest whole mg if you like.
2. Now copy that table of values into Google Sheets and create a scatter plot. Have Google Sheets find an exponential “trendline” equation for this data set, and write it here. You do not need to include this spreadsheet with your submission. (Note: you’ll have to add the “y=” in front of what Google Sheets gives you.)
3. a) Come up with your own exponential equation to model the drug level in the patient’s body, based on the information given in the first paragraph at the top of this page.
b) Comment on the differences and similarities between your equation and the one from Google Sheets.
4. Once the amount of the drug in the patient’s body has decreased to below 5 mg, it is time for another dose. How often should the patient be taking this dose of the drug? Round to the nearest hour. (Note: You can figure this out any way you want—just make sure you document it! You can use either your equation or the one from Google Sheets.)
Part 2:
Ryan, a furniture salesman, is offered two choices for his method of compensation. With Option A, he makes $2500 per month plus a 7% commission on his sales that month (so, for example, if he sold $100,000 in furniture, he’d make $7000 in commission for a total of $9500 that month). With Option B, he only makes commission, but it is 20% of his sales.
1. (w) Come up with a linear model for each option that relates his monthly earnings (A or B, as appropriate) to the value of the furniture he sells in a month (x).
A =
B =
2. Use your equations to fill out the blank cells in the table below.
3. Use your table to help you graph two lines below: one for Option A and one for Option B. (Start by carefully graphing the five points you found in the table for each line.) Please note that this graph needs to be completed by you, and not a spreadsheet, in order to earn credit. Then use your graph to determine approximately when Option B will give Ryan a higher income.
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