Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by ½ each week for a number of weeks, w. He writes the expression 20(⅖) to find the amount of radioactive substance remaining after w weeks.
The expression 20(⅖) represents the amount of radioactive substance remaining after w weeks.
To understand this expression, let's break it down step by step:
Step 1: Start with the initial amount of radioactive substance, which is 20 milligrams.
Step 2: Each week, the amount of radioactive substance decreases by ½. This means that after the first week, only ½ of the original amount remains (20 * ½ = 10).
Step 3: The fraction ⅖ indicates that after every subsequent week, only ⅖ of the remaining amount remains. So, after the second week, 10 * ⅖ = 4 milligrams remain.
Step 4: We can continue this pattern for any number of weeks (w), applying the same concept. For example, after 3 weeks, the expression would be 20 * ½ * ⅖ * ⅖ = 1.6 milligrams.
Therefore, the expression 20(⅖) represents the amount of radioactive substance remaining after w weeks.