Creating an exponential equation

[TN17]

Homework Statement

A bacteria culture starts with 3000 bacteria.
After 3 h, the estimated counting is 48 000. What is the doubling period?

The Attempt at a Solution

I figured it would look like the half-life formula, so I wrote it as:

B = B₀(0.5)^t/h
Then I subbed numbers in:
48 000 = 3000(0.5)^3/h
16 = 3/h (log0.5)
h = 3 (log0.5/log16)
h = -0.75

The answer at the back was 3/4 h, but I don't know if I did it correctly. I don't think the (-) makes sense.

 

[Coto]

Replace 0.5 with 2... i.e replace "half life" with "doubling".

 

[HallsofIvy]

Coto is exactly right. Note, by the way, that 48000 is 16 times 3000 so in 3 hours it has far more than doubled- the doubling time is less than 3 hours not more.

Which means, in fact, that you answer is correct- it has doubled 4 times in 3 hours. The doubling time is 3/4 hours. You have a negative sign because
$$\left(\frac{1}{2}\right)^{-1}= 2$$