Natalie performs a decay simulation using small colored candies with a letter printed on one side. She starts with 200 candies and pours them onto a plate. She removes all the candies with the letter facing up, counts the remaining candies, and then repeats the experiment using the remaining candies. Here are her data for each stage:

After stage 6, she checked the remaining candies and found that seven did not have a letter on either side.
a. Natalie uses the point-ratio equation, y = y1 ( bx-x1, to model her data. What must she do to the equation to account for the seven unmarked candies? Write the equation.
b. Natalie uses the second data point, (1, 105), as (x1, y1). Write her equation with this point and then solve for b in terms of x and y.
c. Make a table that shows the values Natalie gets for b when substituting the other coordinates into the equation from 5b.
d. How should Natalie choose a value for b? What is her model for the data? Graph the equation with the data, and verify that the model fits reasonably well.

Stage number 0 123 456 Candies remaining 200 105 57 31 1814 12