1. ## Expoments question

How would one set this word problem as an equation?

A piece of wood burns completely in one second at 600C. The time the wood takes to burn is doubled for every 10C drop in temperature and halved for every 10C increase in temperature. In how many seconds would the wood burn at

a) 500C b)650C

I've just gotten started working with exponents so I only have a basic understanding of the doubling function, and that doesn't help much...

2. Originally Posted by DemonX01
How would one set this word problem as an equation?

A piece of wood burns completely in one second at 600C. The time the wood takes to burn is doubled for every 10C drop in temperature and halved for every 10C increase in temperature. In how many seconds would the wood burn at

a) 500C b)650C

I've just gotten started working with exponents so I only have a basic understanding of the doubling function, and that doesn't help much...
At 500C, the temperature has dropped 100 degrees from 600 C. That is 10*10 so the time, starting at 1 second, is doubled 10 times. "Doubling 10 times" is $2^{10}$.

At 650C, the temperature has increased by 50 degrees from 600 C. That is 10*5 so the time, starting at 1 second, has halved 5 times. "Halving 5 times" is $(\frac{1}{2})^5$.

3. Thanks. That was what I did for the 500C part and it was right, but when I did the same for the 650C part, the answer showed differently. The answer evaluated to (1/2)^4=1/32, instead of (1/2)^5.

$\left(\frac{1}{2}\right)^4= \frac{1}{16}$.
$\left(\frac{1}{2}\right)^5= \frac{1}{32}$.