Question

10. A perfect circle measuring 38 feet across was discovered on Brickell Avenue in Miami in 1998. Known as the Miami Circle at Brickell, it is believed to be a structure built by the Tequesta Indians. Pieces of burnt wood were found at the site and carbon- 14 dating was used to determine the age of the site. The wood chips were found to contain 80% of the atmospheric carbon-14. Calculate the age of the wood chips to verify the approximate age of the Tequesta settlement. Show your work.

Answer 1

Using an exponential function, it is found that the Tequesta settlement is 1845 years old.

What is an exponential function?

The exponential equation for a decaying amount of a substance is given by:

$A(t) = A(0)e^{-rt}$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

$A(t) = A(0)e^{-rt}$

$0.5A(0) = A(0)e^{-5730r}$

$e^{-5730r} = 0.5$

$\ln{e^{-5730r}} = \ln{0.5}$

$5730r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{5730}$

$r = 0.00012096809$

Hence, the equation is:

$A(t) = A(0)e^{-0.00012096809t}$

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

$A(t) = A(0)e^{-0.00012096809t}$

$0.8A(0) = A(0)e^{-0.00012096809t}$

$e^{-0.00012096809t} = 0.8$

$\ln{e^{-0.00012096809t}} = \ln{0.8}$

$-0.00012096809t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{0.00012096809}$

$t = 1845$

The Tequesta settlement is 1845 years old.

You can learn more about exponential functions at brainly.com/question/25537936