Problema Solution
a certain bacterial culture is multiplying in a culture dish doubling in size every 10 minutes it takes 2 hours to fill the whole dish how long does it take to fill half of the dish
Answer provided by our tutors
we use the following formula for exponential growth:
a(1+r)^t
where 'a' is the initial amount, 'r' is the rate of growth and 't' is the time growth continues
we have r=2, 'a' is unknown and we want to solve for 't' when the growth is half of "a(1+2)^2"
let 't' represent the time at which half the dish has been filled, then:
a(1+2)^t = (a/2)(1+2)^2
(3)^t = 4.5
t = 1.367
it takes approximately 1.4 hours to fill half of the dish