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

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