Math problem!?

Question

If a person has contracts a bacteria, and each bacteria divides every 20 minutes, how many will they have after 40 hours?

The example they gave is this:
20 min: 2
40 min: 4
80 min: 8
etc.

I can't think of a way to do this without a long and very painful process, so please show me your work for it! Thanks!

Answer 1

2^3h, where h is the number of hours, including fractional parts. So after 40 hours = 2^120 = 1.329 x 10^36

BTW, in your example it s/b 60 min = 8

Answer 2

Each hour has 3 units of 20 minutes. In 40 hours there are 120 units of 20 minutes.
Each time the bacteria doubles it will add an exponent to 2.
For example
after 1 unit (20 min) it is 2^1= 2
after 2 units (40 min) it is 2^2= 4
after 3 units (80 min) it is 2^3 = 8
after 4 units (120 min) it is 2^4= 16

after 120 units (40 hrs) it is 2^120
Use your calculator and the answer is 1.3292279957849158729038070602803e+36

Answer 3

For each 20 minute period, the number of bacteria doubles. So first determine how many 20 minute periods are in the 40 hr timespan. Since each hour has three 20-minute timespans, 40 hours would consist of 120 such timespans.

So you'd basically double 120 times. Each time you double is multiplying by 2. So the process comes down to multiplying by 2 and doing it a 120 times, which is the same as 2 to the power of 120 - i.e. 2¹²º = a very very large number (use a calculator to compute the answer).

Answer 4

the bacteria divides, or double, every 20 minutes. This is an exponential function

A = P(r)^(t)

for the t, since the bacteria doubles every 20 minutes, it's gonna be t/20, where t represents time in minutes

At the 0, the amount of bacteria is 1. 20 minutes later, the amount is 2

A = 1(2)^(t/20)

40hrs = 2400 minutes

A = 1(2)^(2400/20)
A =~ 1.329 x 10^36 bacteria

Answer 5

wow I found it! it is actually very simple. Just divide the minutes by ten to get the number of bacteria.
the answer is 240 bacteria because 40 x 60= 2400 and 2400/10=240

Answer 6

do a proportion, 2/20=x/2400. The 2400 is 40 hours in min 60 times 40. cross multiple so 20x=4800. Divide both sides by 20 to get x by itself. so x =240

Answer 7

40 hours(60min/hr) = 2400 min
2400 min /20min/division = 120 divisions
the bacteria divides 120 times
you will have 2^120 = 1.3292279 x 10^36 bacteria in 40 hours.

Answer 8

20 min = (1/3) hours

40 hours has 120 periods of 1/3 hours each

2^120 = 1.32923E+36

Answer 9

In 1hr there are 3 20min time intervals.
40hr = 120 of them, so it would have the chance to divide 120 times, each time giving you twice as many the previous interval.

Just do 2^120.
That's what I'd do. :)

Answer 10

40hours/20min = 120.

so there are bacteria of 2 raised to the 120th power .