Question

Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?

Answer 1

8.2 units of radioactive material will remain after 10 hours

Explanation:

Given :
`f(x)=10(0.98)^(x)`

To Find : , how much radioactive material will remain after 10 hours?

Solution :

Since we are given a function that represents the amount of radioactive material remaining in a medical waste container over time.

`f(x)=10(0.98)^(x)`

Where x denoted hours

Since we are asked to find the amount of radioactive after 10 hours .

So, put x = 10 in the given function

`f(10)=10(0.98)^(10)`

`f(10)=10*0.8170`

`f(10)=8.170`

Thus f(10)=8.17 ≈ 8.2

Hence 8.2 units of radioactive material will remain after 10 hours

Answer 2

For radioactive decay, the amount should decrease over time. Given the function:

`f(x)=10(0.98)^x`
We substitute the time of x = 10 hours:

`f(10)=10(0.98)^(10) \\ f(10) = 8.17`
Therefore 8.2 units will remain after 10 hours.