An anthropologist finds bone that her instruments measure it as 0.012% of the amount of carbon-14 the bones would have contained when the person was alive. how long ago did the person die?
the half life of carbon 14 is 5,730 years. round your answer to the nearest thousand.(35pts).

It can be calculated using the equation:

  = decimal amount remaining, where n is a number of half-lives.

Decimal amount remaining is 0.00012 (= 0.012%). Let's calculate number of half-lives.

⇒ 

⇒ 

⇒ n ≈ 13

Now we know that number of half-lives is 13.

Number of half-lives is quotient of total time elapsed and length of half-life.
So, total time elapsed is a product of length of half-life (5,730 years) and number of half-lives (13). Since 5,730 years × 13 = 74,490 years, then the person died 74,000 years ago (rounded to the nearest thousand).

$8,000 was loaned at a 9% interest rate

Step-by-step explanation:

Ok, so we know the bank loaned part of the $17,500 at a 4% interest rate.  Lets call this loan amount x.  Then the rest of the 17,500 was loaned at a 9% interest rate.  Whatever this amount was, we can define it as 17,500 - x.  We also know that the total interest earned was $1,100.  With this information, we can form the following equation:

.04(x) + .09(17500 - x) = 1100

Multiply the .09 times the inside of the parentheses:

.04x + 1575 - .09x = 1100

Simplify:

-.05x + 1575 = 1100

-.05x = -475

x = 9500

Since x is originally the amount loaned at the 4% interest rate, we know that $9,500 was loaned at a 4% interest rate.

To figure out the other amount loaned at 9%, simply subtract 9,500 from 17,500 -- this gets us 8,000.  So $8,000 was loaned at a 9% interest rate.