Find exponential equation matching data

Question

The table below shows the number of people in an arena t minutes after an event has ended.

T= minutes after event ended: 4 8 12 16 20 24

F(t)= number of people in area: 15221 10649 7375 4859 3468 2285

-Use the regression capability of your graphing calculator to find an exponential equation matching this data. Round values to three decimal places.

F(T)= ___

-use your equation (with values rounded to three decimal places) to help you answer the following questions.

(Note: do not use the data table to answer these questions) Round your answers to the nearest whole number.

-  How many people were in the arena 23 minutes after the event ended?

-How many people were in the arena 60 minutes after the event ended? 

 How many people were in the arena at the exact moment the event ended?

Answer 1

Assuming you have a TI-84 Plus CE:

1) Push the "stat" button (4 buttons up from the "8"). The "EDIT" will be highlighted and "1:Edit" will be highlighted. Push "enter".

2) This will take you to your calculator's "list". It is a table of values with headers that say L₁, L₂, L₃, etc. Make sure it is empty. If it has data in it, use your cursor buttons to scroll to the header row and then scroll to the column the has data. For instance, if there is data in column L1, scroll to L1 until it is highlighted. Press "clear" then "enter" and that column clears out. Repeat as necessary to clear the lists. Then scroll to the top of the first column, just under "L₁" and begin typing in all your data so it looks like this:

3) Push "stat", use your cursor button to scroll right to "CALC", use your cursor button to scroll down to "0:ExpReg" and hit "enter". You will get a screen that looks like this:

ExpReg

Xlist: L1

Ylist: L2

FreqList:

Store RegEQ:

Calculate

Scroll down to highlight "Calculate" and push "enter"

4) The answer appears. You will see a screen that says:

y = a*b^x

a = (a certain number)

b = (another certain number)

(I'll let you get your own answer. Please note that "a" is a big number and "b" is a number smaller than 1)

This is the answer to the first question. For instance, if a = 20000 and b = 0.9 then F(t) = 20000•0.9^x

To answer the other questions, use your equation above and plug in t = 23, t = 60, and t = 0 to get the answers. Do not round off the values of "a" and "b" but once you get each answer, round it to the nearest whole number.