contestada

The radioactive substance cesium-137 has a half-life of 30 years. The amount At (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function. At = 523(1/2)^t/30 Find the initial amount in the sample and the amount remaining after 100 years. Round your answers to the nearest gram as necessary.
Initial amount: grams
Amount after 100 years: grams

Respuesta :

princessesther2011

Answer:

Initial amount is 523 grams

Amount after 100 years is 52 grams

Step-by-step explanation:

General exponential function for radioactive substances is given by

A(t) = Ao(1/2)^t/t1/2

Where,

A(t) is the amount remaining after t years

Ao is the initial amount of the radioactive substance

t is the number of years required for the radioactive substance to decay to A

t1/2 is the half-life of the radioactive substance

Comparing A(t) = 523(1/2)^t/30 with the general exponential function

Initial amount (Ao) = 523 grams

A(t) = 523(1/2)^t/30

t = 100

A(100) = 523(1/2)^100/30 = 523×0.5^3.333 = 523×0.0992 = 51.8816 = 52 grams (to the nearest gram)

Eduard22sly

A. The initial amount of the radioactive substance (cesium-137) obtained from the question is 523 g

B. The amount of the radioactive substance remaining after 100 years is 52 g

Data obtained from the question

  • Aₜ = 523(1/2)^t/30
  • Half-life (t½) = 30 years
  • Time (t) = 100 years
  • Initial amount (A₀) =?
  • Amount remaining (Aₜ) =?

A. How to determine the initial amount

The general formula is given as follow

Aₜ = A₀(1/2)^t/t½

Where

A₀ is the initial amount

Aₜ is the amount remaining at time t

t is the time

t½ is the half-life

Comparison

Aₜ = A₀(1/2)^t/t½

Aₜ = 523(1/2)^t/30,

Initial amount (A₀) = 523 g

B. How to determine the amount remaining

  • Initial amount (A₀) = 523 g
  • Time (t) = 100 years
  • Time (t) = 100 years
  • Amount remaining (Aₜ) =?

Aₜ = A₀(1/2)^t/t½

Aₜ = 523(1/2)^100/30

Aₜ = 52 g

Learn more about half life:

https://brainly.com/question/26374513

Otras preguntas