The number of mold spores in a petri dish increases by a factor of 10 every week. If there are initially 40 spores in the dish, how long will it take for there to be 2000 spores?
5 days, 22 hours ( to the nearest hour )
We need to find an equation of the form:
From the given information we know the initial amount is 40.
If they are increasing by a factor of 10 every week, then we would expect the amount after 1 week to be 400. So, using our equation:
We need to solve this to find the growth/decay factor
Divide both sides by 40:
Taking natural logs of both sides:
Now we know
Final amount is
Using the fact that
Divide by 40:
Taking logs of both sides:
or 5 days, 22 hours ( to the nearest hour )
We wouldn't expect this to be exact, because we rounded to 4 dp.