SOLUTION: A scientist is monitoring cell division and notes that a single cell divides into 4 cells within one hour. During the next hour, each of these cells divides into 4 cells. This proc

Algebra ->  Functions -> SOLUTION: A scientist is monitoring cell division and notes that a single cell divides into 4 cells within one hour. During the next hour, each of these cells divides into 4 cells. This proc      Log On


   

Question 1202248: A scientist is monitoring cell division and notes that a single cell divides into 4 cells within one hour. During the next hour, each of these cells divides into 4 cells. This process continues at the same rate every hour.
Part A. What type of function could be used to represent this situation?
Part B. Justify your reasoning.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This is an exponential function because the number of cells quadruple each hour. We multiply the previous cell count by 4 to get the new cell count.

1 cell -> 4 cells -> 16 cells -> 64 cells -> etc

A visual representation could be a tree diagram such as this example

Generation A = 1 cell
Generation B = 4 cells
Generation C = 16 cells
And so on.

The equation would be
y = 1*4^x
or simply
y = 4^x
where,
x = number of hours
y = number of cells

Example: if x = 2 hours elapse then y = 4^x = 4^2 = 16 cells are present (see generation C in the diagram above)