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.
- 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.
- 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.
- 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.
- What do you notice about the change in the prediction between and ?
- 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.