# 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?

##### 2 Answers

Apr 5, 2016

#### Explanation:

After 1' the count is 2. After 2', the count is

The count after N minutes is

For cell-division arithmetic, double-precision format is a must.

Apr 5, 2016

#### 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=(2)^16#

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