The duration of 5700 years is referred to as the "half-life" of carbon-14 because the amount of carbon-14 drops in half 5700 years after any starting point (not just years). Verify this property by comparing the amount of remaining carbon-14 after 11,400 years and 17,100 years. Write the corresponding expression for the remaining fraction of uranium-234, which has a half-life of about 80,000 years.

Step-by-step explanation:

Given:

Carbon-14

t1/2 = 5700 years

t1 = 11400 years

t2 = 17100 years

N(t) = No(1/2)^(t/t1/2)

Where,

N(t) = amount of carbon left at time, t

No = initial amount of carbon

t = time taken

t1/2 = half life

Assume No = 1

N(11400) = 1 × (1/2)^(11400/5700)

= (1/2)^2

= 1/4

N(17100) = 1 × (1/2)^(17100/5700)

= (1/2)^3

= 1/8

From the fractions got from N(11400) and N(17100), 1/4 and 1/8 we can see a decrease in the initial amount of carbon by 1/2.

B.

t1/2 = 80000 years

N(t) = No × (1/2)^(t/80000)

Assume No = 1

N(t) = 1 × (1/2)^(t/80000)

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.