Question

Bacteria grow by cell division. If each cell divides into 2 in every 2 minutes how many cells will exist after 32 minutes? Assume there was only one cell at the beginning?

Answer 1

`(2)^(2^31)= 2^2147483648`.

Explanation:

After 1' the count is 2. After 2', the count is `2^(2^1)`, and so on. . After, 32 minutes, the cell population will be
`(....((((2^2)^2)^2)^2)...31 times)`
`=(2)^(2^31)`
The count after N minutes is `(2)^(2^(N-1))`.
For cell-division arithmetic, double-precision format is a must.

Answer 2

`65536` cells

Explanation:

Use the exponential growth formula:

#color(blue)(|bar(ul(color(white)(a/a)y=a(b)^(t/d)color(white)(a/a) |)))#

where:
`y=`final amount
`a=`inital amount
`b=`exponential growth
`y=`time elapsed
`d=`doubling-time

Start by setting up the equation.

In your case:

• `y=`unknown
• `a=1` (starts with `1` cell)
• `b=2` (represents doubling of population)
• `t=32` (how long bacteria population doubles for - `32` minutes)
• `d=2` (doubling-time of `2` minutes)

Thus:

`y=a(b)^(t/d)`

`y=1(2)^(32/2)`

Solve for `y`.

`y=(2)^16`

`color(green)(|bar(ul(color(white)(a/a)y=65536color(white)(a/a)|)))`

`:.`, `65535` cells exist after `32` minutes.