(1 point) A radioactive material's half life is 10 hours. There were 49 grams of this material initially. Answer the following question. There would be $\square$ grams left after 20 hours. Round your answer to two decimal places.
Solution
Step 1 ：Given that the initial amount of the radioactive material is 49 grams, the half-life is 10 hours, and we want to find the remaining amount after 20 hours.
Step 2 ：First, calculate the number of half-lives that have passed. This is done by dividing the total time by the half-life. In this case, \( \frac{20}{10} = 2 \) half-lives have passed.
Step 3 ：Next, calculate the remaining amount of the radioactive material. This is done by dividing the initial amount by \(2\) raised to the power of the number of half-lives that have passed. In this case, \( \frac{49}{2^2} = 12.25 \) grams.
Step 4 ：So, after 20 hours, which is two half-lives, there would be 12.25 grams of the radioactive material left.
Step 5 ：Final Answer: There would be \( \boxed{12.25} \) grams left after 20 hours.
