Maths functions question
2 answers:
Answer:
-4 < x < 3
Step-by-step explanation:
<u>Information from Parts 1-4 of the same question:</u>
- A = (3, 0)
<u>Information from Parts 5-8 of the same question:</u>
- D = (-4, 7)
The values of x for which g(x) < f(x) are the values of x between the points of intersection of the two functions: points D and A.
From part (2) of the question, we found that A = (3, 0).
From part (5) of the question, we found that D = (-4, 7).
Therefore, the values of x for which g(x) < f(x) are -4 < x < 3.
In interval notation this is: (-4, 3).
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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;