Carbon Dating: Use the formula y= ae^-.00012t where a is the initial amount of carbon-14 , t is the number of years ago the animal lived, and y is the remaining amount after t years
how old is a fossil remain that has lost 95% of its carbon-14
To determine the age of the fossil remain, we need to find the value of t in the equation y = ae^(-0.00012t) when y is equal to 0.05.
First, let's understand the equation. In this equation, y represents the remaining amount of carbon-14 after t years, a is the initial amount of carbon-14 in the fossil, and the constant -0.00012 represents the rate of decay of carbon-14 over time.
To find the age of the fossil, we need to solve the equation for t when y = 0.05. Let's substitute these values into the equation:
0.05 = ae^(-0.00012t)
Divide both sides of the equation by a:
0.05/a = e^(-0.00012t)
To isolate t, we need to take the natural logarithm (ln) of both sides:
ln(0.05/a) = ln(e^(-0.00012t))
Applying the logarithmic property ln(e^x) = x:
ln(0.05/a) = -0.00012t
Now, we can solve for t by dividing both sides of the equation by -0.00012:
t = ln(0.05/a) / -0.00012
To find the age, you need to know the initial amount of carbon-14 (a) in the fossil. Let's assume it is a known value, and substitute that into the equation. For example, if the initial amount of carbon-14 is 100 units:
t = ln(0.05/100) / -0.00012
Calculating this expression will give us the value of t, which represents how many years ago the animal lived.