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

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

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.