# Thread: Help with Exponential Growth...

1. ## Help with Exponential Growth...

Hello-
I need some help with the problem below. You help is greatly appreciated.

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?

2. Originally Posted by Cori1984
Hello-
I need some help with the problem below. You help is greatly appreciated.

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?
$f(t) = 0.01 \cdot 2^t$

You should be able to plot that graph as a standard exponential

3. Thank you. I'm not sure what you mean though. I received the following hint from the instructor.
HINT: The house cleaning project is an example of exponential growth. The model will look like this y = abx where a is the value of y when x=0 or it can be modeled using A = A0ekt where A0 is the value of the total amount A when t = 0 so when x=t=0 (December 1 no complete days worked) you have in the first model 1=A0e0 so A0 is 1 in the first model now you have A = ekt . In the second model you have 1 = ab0 and a is 1. The second model is y = bx. On December 2, x=t=1 (one complete day worked) and you are paid 2 cents. This means that in the model A=ekt that 2=ek(1). This equation will allow you to solve for k using logs. In the model y=bx when x=1 then y=2. This allows you to solve for b in the model. Once you have solved for all unknows in each model, you can determine the x and y coordinates for both from x =0 to x=20.

4. I'm not sure what you're actually asking, could you make it clearer please?

Normally you'd use ^ for power so aex would be ae^x (or use Latex)