# 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?

##### 1 Answer

5 days, 22 hours ( to the nearest hour )

#### Explanation:

We need to find an equation of the form:

Where

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:

**( ln(e)=1, the logarithm of the base is always 1)
**

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 )

CHECK:

We wouldn't expect this to be exact, because we rounded to 4 dp.