the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 as does living plant material. Determine when the wood was cut

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

(Eq. 1)

Where:

- First derivative of mass in time, measured in miligrams per year.

- Time constant, measured in years.

- Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

(Eq. 2)

Where:

- Initial mass of isotope, measured in miligrams.

- Time, measured in years.

And time is cleared within the equation:

Then, time constant can be found as a function of half-life:

(Eq. 3)

If we know that and , then:

The wood was cut approximately 8679 years ago.

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.