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olga nikolaevna [1]
3 years ago
7

Two qualities, x and y, if x is doubled what happends to y?​

Mathematics
1 answer:
sukhopar [10]3 years ago
7 0

Answer:

it gets doubled too bc if one quantity is doubled then the other is too

Step-by-step explanation:

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Radioactive isotopes are commonly used to estimate artifact ages. Let X be the time in years for a Carbon-14 atom to decay to Ni
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Answer:

a) 1 / years

b) P ( 5000 < X < 6000) =  0.06222

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d) T_1/2 = 5730.25 years          

Step-by-step explanation:

Given:

- The decay constant λ = 1 / 8267

- X is an exponential random Variable

Find:

a. What are the units of What are the units of λ?

b. What is the probability the decay time is between 5000 and 6000 years?

c. Compute SD(X).

d. Compute the median decay time. The result is called the half-life of Carbon-14?

Solution:

- The decay constant λ means the rate at which the C-14 atoms decays into N-14 atom. The rate is expressed in units of 1 / year.

- The random variable X follows an exponential distribution which has a probability mass function and cumulative density functions as follows:

                    P ( X = t ) = λ*e^(-λ*t)

                    P ( X = t ) = e^(-t/8267) / 8267

                    P ( X < t ) = 1 - e^(-λ*t) = 1 - e^(-t/8267)

- The probability of the decay time between years 5000 and 6000 years is:

                    P ( 5000 < X < 6000) = 1 - e^(-6000/8267) - 1 + e^(-5000/8267)

                    P ( 5000 < X < 6000) =  0.06222

- The standard deviation of the exponential distribution is given by:

                    SD(X) = 1 / λ = 8267 years

- The median decay time for an exponential distribution is given by:

                    T_1/2 = Ln(2) / λ = Ln(2)*8267

                    T_1/2 = 5730.25 years                        

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