the number of bacteria in a culture increases by 20% every 20 minutes. If there are 1,000 bacteria present at noon on a given day, to the nearest thousand, how many will be present at midnight of the same day?

Question

anonymous · Answer

you can us $$p = p _{0}e ^{rt}$$

P = Total population after time
$$P_{o}$$ = starting population
r = % of growth rate
T = Time in hours or years
and e = Euler number

exoexoexo · Answer

what is an euler number?

anonymous · Answer

it's e on your calculator and it is a constant like pi   e = 2.71828....

anonymous · Answer

alternatively you since this also creates a geometric sequence you can just calculate it like this
$$1000(1.2)^{36}$$

anonymous · Answer

since noon to midnight is composed of 36, 20 minute intervals. and the common ratio is 1.2

anonymous · Answer

whichever way you like best :)

danjs · Answer

you see the form of this type of growth looks like

Number Bacteria = (some start value at t=0) * (ratio of change) 


every 20 min, the bacteria are multiplied by that (ratio of change) , that is why this is an exponential growth

Number Bacteria = (some start value at t=0) * (ratio of change)^(# of time intervals)

danjs · Answer

define noon to be time t=0, and then the bacteria = 1000

y = 1000 * (120/100)^x

danjs · Answer

The number increases to 120% of the previous, or, grows by 20%,  every 20 min,  

the power x is then multiples of 20 min, or just say that is 1/3 hour, and let x be in hours
Increases by 20% every 1/3 hour

danjs · Answer

so the power is then (3x)  if you let x be hours,   every hour, increases 3 times,