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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?

Verified Answer :

Blitztiger

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.

Answer:

8.2 units of radioactive material will remain after 10 hours

Step-by-step 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

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