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?

0.8 units
1.3 units
8.2 units
9.8 units

Explanation:

Identify the function and given value

$$ f(x) = 10(0.98)^x,\quad x = 10 $$

Evaluate the exponential expression

$$ f(10) = 10(0.98)^{10} \approx 10(0.81707) = 8.1707 $$

Round to the nearest tenth

$$ f(10) \approx 8.2\text{ units} $$

Answer:

• 0.8 units
• 1.3 units
• 8.2 units (Correct answer)
• 9.8 units