Graphing exponential functions

Mar 2017
356
3
Massachusetts
Hi,

I hope someone can help.

I'm trying to calculate what the instantaneous rate of change would be at year 2 for the following table:

Screen Shot 2017-06-20 at 6.24.26 PM.png

I'm suppose to plot these points on a graphing calculator and then find the values of y (students per computer) that are close to year 2, then use these points to calculate the instantaneous rate of change. The only problem is that I don't have a graphing calculate on hand that has the power to do this. Are there any only resources that could be a close substitute? Please let me know.
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
Data does not model an exponential function, rather a power function.

Conducted a power regression at this online site ...

Power regression Calculator - High accuracy calculation

A power regression is of the form $y = Ax^B$. You may input the data from the table and conduct it again if you like.

regression results attached ...

Instantaneous rate of change in units of (students per computer)/(year) at year 2 is $\approx -35$
 

Attachments

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
I don't understand what you would expect a calculator to do for you. The x values "closest to 2" are x= 1, x= 2, and x= 3. The "difference quotient" between x= 1 and x= 2 is \(\displaystyle \frac{75- 125}{2- 1}= -\frac{50}{1}= -50\). The "difference quotient" between x= 2 and x= 3 is \(\displaystyle \frac{50- 75}{3- 2}= -\frac{25}{1}= -25\). You can combine those and so an get an approximate derivative at 2 by averaging them: \(\displaystyle \frac{-25- 50}{2}= -\frac{75}{2}\).
 
Mar 2017
356
3
Massachusetts
Okay all the responses above make sense. I got the same results as well. I think my textbook is just wrong because it says that the answer is -12.378.
 
Mar 2017
356
3
Massachusetts
since the textbook was wrong about instantaneous rate of change (IROC) at year 3, can someone please confirm with me what the IROC was at year 2 and 7?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
since the textbook was wrong about instantaneous rate of change (IROC) at year 3, can someone please confirm with me what the IROC was at year 2 and 7?
... your original post asked about the rate of change at year 2.

The rate of change for year 3 should be in the neighborhood of -19

The rate of change for year 7 should be in the neighborhood of -2.5