A cell phone is plugged in to be charged. The table shows the percentage of battery power at some times after the phone was plugged in.

1. The image shows the battery usage of a cell phone for 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 percentage of battery power, , as a function of time since the phone was fully charged, . Show your reasoning.

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

   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? Show your reasoning.
2. Here are two more images showing the battery usage at two later times, before the battery was charged again.

   

   Two images of advanced battery usage, 29 percent and 7 percent. 29 percent shows a graph of usage from 100 percent to 0 percent. States 13 hours ago, 4 hours left. 7 percent shows a graph of usage from 100 percent to 0 percent. States 14 hours ago, 29 minutes left.

   1. 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)? Explain or show your reasoning.
   2. What do you notice about the change in the prediction at  and at  ?
   3. Write a new equation for a function that would better fit the data shown in the last image.