CPM Homework Help : INT1 Problem 8-108

Eeeeew! Hannah’s volleyball team left their egg salad sandwiches sitting in their lockers over the weekend. When they got back on Monday, they were moldy. “Perfect!” said Hannah. “I can use these sandwiches for my biology project. I’ll study how quickly mold grows.”

Using a transparent grid, Hannah estimated that about $12$ % of the surface of one sandwich had mold on it. She threw the sandwich out. For the rest of the week, Hannah came back when she had time. Each time, she measured somebody else’s sandwich and threw it out. She collected the following data:

Day $1$ (Monday)	Day $2$ (Tuesday)	Day $2$ (Tuesday)	Day $4$ (Thursday)	Day $4$ (Thursday)	Day $4$ (Thursday)	Day $5$ (Friday)
$12$ %	$15$ %	$13$ %	$26$ %	$27$ %	$24$ %	$38$ %

Create a scatterplot and sketch it. Is a linear model reasonable?
Hint (a):
Use a hand held calculator or the Desmos calculator below to graph a scatterplot. Refer to the Math Notes box in Lesson 1.1.2 to help you determine if a linear model is reasonable.
Based on the story, what kind of equation do you think will best fit the situation?
Answer (b):
Exponential growth fits this situation best.
Fit the data with an exponential model and write the equation. What percentage of a sandwich did Hannah predict was covered on Wednesday? Consider the precision of Hannah’s measurements when deciding how many decimal places to use in your answer.
Hint (c):
If you are using the Desmos calculator below use the following steps.
Step 1(c):
Enter the data from line $4$ of the Desmos calculator into the table in line $5$ .
Step 2(c):
In line $7$ enter the regression formula: $M \sim ab^{D}$
To match the TI calculator answers click the Log Mode button on the Desmos calculator.
Answer (c):
$M = 8.187 · 1.338^{D}$
Where:
$M =$ the percent of mold
$D =$ number of days
Hannah predicted the mold covered $20$ % of the sandwich on Wednesday, and she measured to the nearest percent.

Use the eTool below to create a scatterplot.
Click on the link at right for the full eTool version: Int1 8-108 HW eTool