Ok, you know the drill here. we will use the formula:
2. Another newton's cooling problem.
On Easter, a ham is removed from an oven and placed in a room where the temperature is 70 degree F. A meat thermometer indicates that internal temperature of the ham to be 220 degree F. 30 minutes later, the meat thermometer indicates 200 degree F. How much longer it will take to cool the meat to 100 degree F.
...see my previous posts on these types of questions to see how I derived this.
So our equaiton is:
Now just plug in and solve for
When done, you have to subtract 30 from that value, since the question asked how much LONGER it will take to cool to 100 [after 30 mins].
For growth and decay, we use pretty much one formula. The only difference is, in decay, we use a negative exponent. As a mnemonic, I call this the PERT formula, as in the shampoo Pert, if you remember--that was a great invention, saves a lot of time. Anyway, what does PERT mean? See if you can see the word below:3. Grow and Decay
Notice that the left side of the formula spells PERT. In the above formula, (a function of time) is the amount of substance after time , is the initial amount of substance, is the rate of growth, and is the time elapsed. This is known as the formula for Exponential Growth, and is usually used to predict the growth of bacteria and populations.
For the Exponential Decay formula, we simply make the exponent of negative. So for exponential decay:
Note that some books will use different letters for . Other common letters used are .
one more formula you need to know for this topic is:
where is the rate of decay, and is the half-life.
Now on to your question.
Now,The wood of an Egyptian sarcophagus (burial case) is found to contain 63% of the Carbon-14 found in a present-day sample. What is the age of the sarcophagus if the half-life of C14 is 5730 years ?
This s a decay problem, so we use the formula:
So we have:
Now we are not told the amount we have now, or the amount that we started with, so how do we proceed here? Answer: we pick a number. I like to use 1, but any number you pick will work out fine.
So assume we start with a sample containing 1 unit Carbon-14. We now have 63% of that, so now we have 0.63 units of Carbon-14. So we can let , so now we just have to find such that, . Thus, to answer this question, we must solve:
will give you the age of the sample