Carbon-14 decays at a constant rate, so it can be used to determine the age of fossils. in particular, if the original amount of carbon-14 present is a0, then a(t) = a0e-kt can be used find the amount of amount of carbon-14 remaining after t years. given that the half-life of carbon-14 is 5,730 years, what is the value of the decay constant k to 5 decimal places?

Value of the decay constant k = 0.00012

Step-by-step explanation:

Formula to determine the age of the fossils by C-14 decay is given as

where A(t) = C-14 remaining after t years

A0 = original amount of C-14

K = decay constant

t = time taken for decay

Now we have to calculate the value of constant k when half life of C-14 is given as 5730 years.

Since half life has been given therefore final amount after 5730 years will be A/2 and initial amount will be A.

Now the equation becomes as

Now by taking natural log on both the sides

ln 1 - ln2 = -5730k (since lne = 1)

0 - ln2 = -5730k

k = 0.00012

Therefore k = 0.00012 is the answer.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50