A culture of bacteria obeys the law of unlimited growth. If 500 bacteria are present initially and there are 800 after 1 hour, how many will be present in the cultrue after 5 hours? How long until there are 20,000 bacteria?
Hmmm, what is "the law of unlimited growth"? In any case, this looks like exponential growth to me.
The most basic formula for exponential growth is
A = P*er*t where r is the rate of growth, t is the time, P is the initial amount and A is observed growth.
Here 800 = 500*er*1hr so
ln(1.6units) = r*1hr or ln(1.6units)/1hr = r or
A = 500*(1.6)t
Substitute 5 for t to answer the first question, i.e.
A = 500*(1.6)5
To answer the second part set A=20,000
20,000=500*(1.6)t or
40 = (1.6)t
It looks to be slightly less than 8 hrs. You can verify this.
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A ship, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation if found to be 25◦, how far offshore is the ship?
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