For questions 1 – 2 , use the following prompt and image.

The image shows the battery usage of a cell phone 9 hours after it was fully charged. It also shows a prediction that the battery would last 8 more hours.

1. Write an equation for a model that fits the data in the image and gives the percent of battery power as a function of time since the phone was fully charged. Be prepared to show your reasoning.

2. Based on your function, what percentage of power would the battery have 4 hours after this image was taken? What about 5 hours after the image was taken? Be prepared to show your reasoning.

For questions 3 – 5, use the following prompt and images.

Here are two more images showing the battery usage at two later times, before the battery was charged again.

3. How well did the function you wrote predict the battery power 4 and 5 hours after the first image was taken (that is, 13 and 14 hours after the battery was fully charged)? Be prepared to show your reasoning.

4. What do you notice about the change in the prediction between $t=13$ and $t=14$?

5. Write a new equation for a function that would better fit the data shown in the last image.

If you get stuck, consider creating a table of values or a scatter plot of the data.