Can someone help me with this please, thanks a lot!!

[eco&math=die]

A piece of wood is recovered from an ancient building during an archaeological
excavation. The formula A(t) 5 A0e20.000 124t is used to determine the age of the wood,
where A0 is the amount of carbon in any living tree, A(t) is the amount of carbon in the
wood being dated and t is the age of the wood in years. For the ancient piece of wood
it is found that A(t) is 79% of the amount of the carbon in a living tree. How old is the
piece of wood, to the nearest 100 years?

 

[Dr.Peterson]

A piece of wood is recovered from an ancient building during an archaeological
excavation. The formula A(t) 5 A0e20.000 124t is used to determine the age of the wood,
where A0 is the amount of carbon in any living tree, A(t) is the amount of carbon in the
wood being dated and t is the age of the wood in years. For the ancient piece of wood
it is found that A(t) is 79% of the amount of the carbon in a living tree. How old is the
piece of wood, to the nearest 100 years?

Yes, we can help. But we need to know what help you need (by seeing how far you got).

I believe the formula given here is supposed to be [imath]A(t)=A_0e^{0.000124t}[/imath], or something like that; the 5 and the initial 2 make no sense to me. It's also odd that they talk about the amount of carbon, not of carbon-14.

 

[eco&math=die]

Thanks for answering. It is my carelessness that the equation should be [math]A(t)=A0e^-0,000124t[/math]. It doesn't say carbon-14, however, I think the question here is talking about carbon-14. This question really makes me confused, hope you can help me again. Thank you.

 

[Dr.Peterson]

Thanks for answering. It is my carelessness that the equation should be [math]A(t)=A0e^-0,000124t[/math]. It doesn't say carbon-14, however, I think the question here is talking about carbon-14. This question really makes me confused, hope you can help me again. Thank you.

So it's really [imath]A(t)=A_0e^{-0.000124t}[/imath].

Are you saying you have no idea how to use this formula? Here's the problem again:

A piece of wood is recovered from an ancient building during an archaeological excavation. The formula [imath]A(t)=A_0e^{-0.000124t}[/imath] is used to determine the age of the wood, where [imath]A_0[/imath] is the amount of carbon in any living tree, [imath]A(t)[/imath] is the amount of carbon in the wood being dated and [imath]t[/imath] is the age of the wood in years. For the ancient piece of wood it is found that [imath]A(t)[/imath] is 79% of the amount of the carbon in a living tree. How old is the piece of wood, to the nearest 100 years?​

Do you see that you are asked to find the value of [imath]t[/imath] so that [imath]A(t)[/imath] will be 79% of [imath]A_0[/imath]? Replace [imath]A(t)[/imath] with [imath]0.79A_0[/imath], and solve for [imath]t[/imath]. Show me whatever you can do, or else tell me what you have been taught about solving such equations.

 

[eco&math=die]

I know how to rewrite the formulate by substituting A(t) with 0.79A0. The point I don't get this is because there are two unknown variables A0 and t. I don't know the initial value of carbon here.

 

[BigBeachBanana]

I know how to rewrite the formulate by substituting A(t) with 0.79A0. The point I don't get this is because there are two unknown variables A0 and t. I don't know the initial value of carbon here.

After the substitution, the term [imath]A_0[/imath] gets canceled on both sides of the equation.
[math].79\sout{A_0}=\sout{A_0}e^{-.000124t}[/math]

 

[eco&math=die]

Ohhhhhhh, thanks!!!!! I'm so dumb