Eeeeew! Hannah left an egg salad sandwich sitting in her locker over the weekend and when she got back on Monday it had started to get moldy. “Perfect!” said Hannah. “I can use this for my biology project. I'll study how quickly mold grows. My hypothesis will be that it grows faster and faster.”  

Hannah knew that first she had to gather data. Using a transparent grid, she estimated that about $12\%$ of the surface of the sandwich had mold on it. She put it back in her locker, and on Tuesday she estimated that $15\%$ was moldy. But then she forgot about it until Friday, when it was about $29\%$ was moldy. Now what? How could she get the missing days data without wasting another sandwich?

“I know,” said Hannah, “I'll use the math I've learned to write an equation that will get me reasonable data.”

1. What type of equation should she use? Justify your answer.

   Answer (a):

   Exponential

2. Write an equation that would estimate the percent of the sandwich that is covered by mold x days after Monday. Remember that your equation will probably not fit perfectly since these are only estimates of data.

   Answer (b):

   $x =$ number of days since Monday

3. How well does your equation “fit” the data?

   Hint (c):

   Test using your function.

4. Use your equation to recreate the data Hannah needed for Wednesday and Thursday. Then predict when the sandwich will be completely covered with mold.

   Hint (d):

   Set $y = 100$ and solve for $x$.