Hi everyone, I'm having trouble with this question and I'm not sure how to do it/where to start. Does anyone have a solution to
it? It will help me with my future problems on this topic!
1 answer:
This is quite an interesting problem. I am not sure how high you are in math, but I am going to use calculus I techniques to solve it. First, we need to model an equation. Let P be the total profit and x be every time you increase the cost by $10. If you think about it hard enough you come up with the equation
(200-5x) is the amount of plots you will be able to sell, and (250+10x) is the amount you charge for. So, at x =0
This is the initial condition where if we sell 200 plots at $250/plot.
So, this equation makes sense.
Now, let's maximize using the first derivative of the function.
Let's get it into an easily differentiable form.
From here, differentiate the problem.
Now, set it equal to zero and solve for x.
This a critical point of the function. Let's plug back into the original equation to see what it gives us.
You cant sell half a plot, so we need to see what happens if we sell 162 plots and 163 plots, and then compare which one gives us more money.
In order to sell 162 plots
Plug back into P(x) to see the profit
Now, do the same for 163 plots
As we can see, they are the same. So, you can charge either $324 or $326 in rent. But, if your teacher is not looking for a logical answer and you can somehow sell half a plot, you can charge $325 in rent for the maximum profit.
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Answer:
1) There are 100 carbon-14 atoms in the wood when it died
2) A function that models the number 'N' of carbon-14 atoms present in the wood (t) years after it died is presented as follows;
Step-by-step explanation:
The given parameters are;
The number of carbon-12 for each carbon-14 atom ≈ 10¹² carbon-12 atoms
The number of carbon-12 in the piece of wood = 10¹⁴ carbon-12 atoms
The number of carbon-14 in the piece of wood = 40 carbon-14 atoms
The number of carbon-12 in an organism = Constant
The number of carbon-14 in an organism = Decays
1) Given that the number of carbon-12 in an organism is constant, and there are 10¹² carbon-12 atoms per each carbon-14 atom, therefore, we have;
The number of carbon-12 atoms in the wood when it died = 10¹⁴ carbon-12 atoms
The number of carbon-14 atoms in the wood when it died = (10¹⁴ carbon-12 atoms)/(10¹² carbon-12 atoms/(carbon-14 atom)) = 100 carbon-14 atoms
The number of carbon-14 atoms in the wood when it died = 100 carbon-14 atoms
2) The half life of a radioactive isotope is given by the following formula;
The half life of carbon-14 atoms, ≈ 5,730 years
N₀ = The amount of carbon-14 present in the wood when it died = 100 carbon-14 atoms
Therefore, we have;
The number, N, of carbon-14 atoms present in the wood (t) years after it died is given as follows;