How can I find the equation for the cell division sequence?

[aisha]

This is an activity to get an introduction to sequences and series it said every hour cells divide

It said there are 500 cells now how many will there be in an hour I wrote 1000 cells

It said to make a table for 5 hours so I got
Hours--Cells
1 ----- 1000
2-------2000
3-------4000
4-------8000
5-------16000

It said create an equation that relates the number of cells and the time I can't see the realationship can someone please help me out!

 

[K.J.Healey]

At some time, choose like 4 hours, look at how the cells are different from the current time 4, and the previous iteration, 3.
Looks to me like it doubles every hour, which is what the problem states.
So maybe something like Cells[t] = Cells[t-1]*2 ??

 

[christinono]

This is an activity to get an introduction to sequences and series it said every hour cells divide

It said there are 500 cells now how many will there be in an hour I wrote 1000 cells

It said to make a table for 5 hours so I got
Hours--Cells
1 ----- 1000
2-------2000
3-------4000
4-------8000
5-------16000

It said create an equation that relates the number of cells and the time I can't see the realationship can someone please help me out!

It looks more to me like an exponential relationship. Hint: the base is 2.

 

[freemind]

Think of what your coefficient for the general iterative form of the sequence will be.

 

[aisha]

Heres what I got I don't know if there is a better way to write it.

Number of cells = 2^\ (t-1) *1000

 

[freemind]

Bravo!

 

[aisha]

Thanks soo much! Any tips on how to know what the relationship is?

 

[dextercioby]

What "relationship" (sic)??Between whom??

Daniel.

 

[freemind]

Usually, your coefficient is the first term of the sequence. As for the base, if you see doubling, it's definitely 2. After that, a little plugging-and-chugging to figure out the exponent doesn't hurt. If you don't see doubling, do what I do and use a CAS. Maple does an amazing job of fitting equations to sequences. I find guessing equations for sequences to be a real pain in the arse, but maybe I'm just too lazy.

 

[aisha]

"do what I do and use a CAS. Maple does an amazing job of fitting equations to sequences." Can you explain what u mean by this?

 

[freemind]

'CAS' stands for "Computer Algebra System", an almost magical computer program that does a variety of mathematical calculations that would otherwise be tedious/impossible/inaccurate by hand. Maple is one of the more popular ones (my 2nd favourite; MATLAB is the simply the best in my experience). Essentially, if you get your hands on one of these things, it will make your academic life a whole lot easier. Oh and all the good ones are proprietary.
You can actually input all the terms of your sequence into Maple and it will puke back the mathematical expression for the sequence. Pretty neat eh?

 

[Curious3141]

'CAS' stands for "Computer Algebra System", an almost magical computer program that does a variety of mathematical calculations that would otherwise be tedious/impossible/inaccurate by hand. Maple is one of the more popular ones (my 2nd favourite; MATLAB is the simply the best in my experience). Essentially, if you get your hands on one of these things, it will make your academic life a whole lot easier. Oh and all the good ones are proprietary.
You can actually input all the terms of your sequence into Maple and it will puke back the mathematical expression for the sequence. Pretty neat eh?

Honestly, I don't think she should be using something like that. It encourages laziness in the same way that overdependence on a calculator does. Besides, nothing she'll be seeing at her level will require anything so abstruse to figure out.