The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milligrams of 14C. Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.

Step-by-step explanation:

The general formula for exponential decay given a half-life is

where N(t) is the amount at time t, is the initial amount (at time t=0), and is the half life of the substance.

The half life of carbon-14, is approximately 5,730 years.

= 5730 years

= 6 milligrams

Therefore:

Amount of carbon-14 remaining in the bone fragment after t years is:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: