A cleaning service will clean your house for the month of December. You will pay the service 1 cent at the beginning of December 1. Let x represent the number of complete days worked. On December 1 the number of complete days worked is zero and x=0, on December 2 one complete day has been worked and x=1, on December 3 two complete days have been worked and x=2 . Y represents the amount paid. On December 1 the amount paid is 1 cent, on December 2 the amount paid is 2 cents, on December 3 the amount paid is 4 cents, on December 4 the amount paid is 8 cents.

Make a table of independent variables (x=complete days worked) and dependent variables (y=amount paid on that date) through t=20.

Choose an appropriate scale for the points to be plotted.

Plot the points using the TI calculator. Copy and paste this scatter plot into your paper using the TI connect. If necessary you can use Winplot. Define a model of uninhibited growth A = A0ekt mathematically.

Use the calculator to define a model of uninhibited growth in the form y = abx . Show that if A=y and t=x then the two functions y = abx and A = A0ekt are the same.

Describe where the graph is increasing, decreasing, or constant. Define the Domain and the Range of the function. How much will you be making on the 15th day? The 20th day?

How much did the cleaning service total over the first 20 days?