Question

what is the original amount of carbon-14 that remains in the sample after t years?p=100(1/2)^t/5730

Answer 1

The equation is

$P=100(\frac{1}{2})^{\frac{t}{5730}}$

To find the original amount of carbon-14 we need to substitute t=0 in our last equation

$\begin{gathered} P(0)=100(\frac{1}{2})^{\frac{0}{5730}} \\ P(0)=100 \end{gathered}$

Then, the original amount of carbon-14 was 100.

To plot the solution, we need to replace the values given in the table

$\begin{gathered} P(2500)=100(\frac{1}{2})^{\frac{2500}{5730}}=73.90 \\ P(5000)=100(\frac{1}{2})^{\frac{5000}{5730}}=54.62 \\ P(7500)=100(\frac{1}{2})^{\frac{7500}{5730}}=40.36 \\ P(8200)=100(\frac{1}{2})^{\frac{8200}{5730}}=37.08 \\ P(10000)=100(\frac{1}{2})^{\frac{10000}{5730}}=29.82 \\ P(12500)=100(\frac{1}{2})^{\frac{12500}{5730}}=22.04 \end{gathered}$

you need to replace this numbers in the table. Then, the graph is