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?\
\
\bigcirc 0.8 units\
\bigcirc 1.3 units\
\bigcirc 8.2 units\
\bigcirc 9.8 units

Explanation:

Step1: Identify the function and input

The function is \( f(x) = 10(0.98)^x \), and we need to find \( f(10) \) (since \( x = 10 \) hours).

Step2: Substitute \( x = 10 \) into the function

\( f(10)=10\times(0.98)^{10} \)
First, calculate \( (0.98)^{10} \). Using a calculator, \( (0.98)^{10}\approx0.8170728 \)
Then, multiply by 10: \( 10\times0.8170728 = 8.170728 \)

Step3: Round to the nearest tenth

Rounding \( 8.170728 \) to the nearest tenth gives \( 8.2 \)

Answer:

8.2 units