2. The level of thorium in a sample decreases by a factor of one-half every 2 million years. A meteorite is discovered to have only 8.6% of its original thorium remaining. How old is the meteorite in millions of years?
2) You need to show how you use the function to solve the problem by showing the following steps:
o What number did you substitute for what term or variable in the function you found above?
o What property did you use to write the exponential equation to a linear equation? (See the properties listed below)
o What property did you use to solve the linear equation and to find the final answer? (See the properties listed below)
(3) You need to state your answer in million years in sentence form.
You many need to use the following properties when you do part (2) to find the age of meteorite in million years:
· a = b^x is equivalent to x = log_b(a)
· log_b(a)= log(a) / log(b)
· If x = y, then log_b(x) = log_b(y)
· x log_b(a) = log_b(a^x)
· log_b(b) = 1
Because of formatting issues, I am using "log_b" to denote "log base b". (In the corresponding announcement, the "b" would appear as a subscript after the "log".)
Respond
Post your question.
To find the age of the meteorite in millions of years, we can use the information given in the problem.
Let's assign variables to the different pieces of information:
- Let t be the age of the meteorite in millions of years.
- Let P be the percentage of original thorium remaining.
According to the problem, the level of thorium in the meteorite decreases by a factor of one-half every 2 million years. This means that the remaining thorium is half of what it was 2 million years ago.
Using this information, we can set up the following equation:
0.5^t = P
Since we know that P is 8.6%, we can substitute it into the equation:
0.5^t = 0.086
To solve for t, we can take the logarithm of both sides of the equation. Using the property log_b(a) = log(a) / log(b), we can rewrite the equation as:
log(0.5^t) = log(0.086) / log(0.5)
By the property x log_b(a) = log_b(a^x), we can simplify the equation further:
t * log(0.5) = log(0.086)
Now, we can solve for t by dividing both sides of the equation by log(0.5):
t = log(0.086) / log(0.5)
Using the property log_b(b) = 1, we can simplify the equation even further:
t = log(0.086) / log(0.5) = log(0.086) / (log(2) / log(10))
Finally, we can calculate the value of t using a calculator or a math software:
t ≈ 7.572
Therefore, the age of the meteorite is approximately 7.572 million years.