This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions for question 10: a) What fraction remains after 6 months? Step 1: Determine the fraction of the amount remaining each month. Each month, half of the remaining amount is given away, so the fraction remaining is (1)/(2). Step 2: Calculate the fraction remaining after 6 months. After 6 months, the fraction remaining will be ((1)/(2))^6. ((1)/(2))^6 = (1^6)/(2^6) = (1)/(64) The fraction remaining after 6 months is (1)/(64). b) What fraction remains after 12 months? Step 1: Calculate the fraction remaining after 12 months. After 12 months, the fraction remaining will be ((1)/(2))^12. ((1)/(2))^12 = 1^122^12 = (1)/(4096) The fraction remaining after 12 months is (1)/(4096). c) Write each fraction as a power of 2 with a negative exponent. Step 1: Express the fraction from part a) as a power of 2 with a negative exponent. (1)/(64) = (1)/(2^6) = 2^-6 Step 2: Express the fraction from part b) as a power of 2 with a negative exponent. (1)/(4096) = (1)/(2^12) = 2^-12 The fractions as powers of 2 with negative exponents are 2^-6 and 2^-12. d) What amount is remaining at the end of the year? Step 1: Identify the initial amount and the fraction remaining at the end of the year. The initial amount is \1\,000\,000. The end of the year means after 12 months. From part b), the fraction remaining is (1)/(4096). Step 2: Calculate the remaining amount. Remaining amount = \1\,000\,000 × (1)/(4096) = (\1\,000\,000)/(4096) = \244.140625 Step 3: Round the amount to two decimal places for currency. ≈ \244.14 The amount remaining at the end of the year is \244.14. That's 2 down. 3 left today — send the next one.