For each carbon-14 atom, there are approximately 10^12 carbon-12 atoms. This ratio is constant in each organism. The carbon-12 remains constant but the carbon-14 decays. Suppose a piece of wood is analysed, and it contains 10^14 carbon-12 atoms and 40 carbon-14 atoms. 1) Determine how many carbon-14 atoms were present in the wood when it died.

2) Use the half life of carbon-14 atoms to obtain a function to model the number N of carbon-14 atoms present in the wood (t) years after it died

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;

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.