Question

PROBLEM SOLVING Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft.The function y=a(0.5)t/x​ represents the amount y​ of a substance remaining after t​ years, where a​ is the initial amount and x​ is the length of the half-life (in years).

Plutonium- 238, Half-life is approximately 88 years.

a. A scientist is studying a 3-gram sample. Write a function that represents the amount y​ of plutonium-238 remaining after t​ years.

Question 2
b. Use the function to estimate the amount of plutonium-238 remaining after 8 years.

Question 3
c. Use the graph of the function to estimate the amount remaining after 12 years.
About grams

Answer 1

The function that represents the amount of Plutonium-238 remaining after t years is y = a(0.5)^t/x. To estimate the amount of Plutonium-238 remaining after 8 years, substitute t = 8 into the equation. Similarly, to estimate the amount remaining after 12 years, substitute t = 12 into the equation.

Step-by-step explanation:

The function that represents the amount of Plutonium-238 remaining after t years is given by the equation:

y = a(0.5)t/x

Given that the initial amount is 3 grams and the half-life is 88 years, we can substitute these values into the equation:

y = 3(0.5)t/88

To estimate the amount of Plutonium-238 remaining after 8 years, substitute t = 8 into the equation:

y = 3(0.5)8/88

Similarly, to estimate the amount remaining after 12 years, substitute t = 12 into the equation:

y = 3(0.5)12/88