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
Step 1: Analyze the given mapping. We are given a set of input values (x) and their corresponding output values (y). For x = 2, y = 4 For x = 3, y = 16 For x = 4, y = 64 For x = 5, y = 256 Step 2: Identify the pattern in the output values. Notice that the output values are powers of 4: 4 = 4^1 16 = 4^2 64 = 4^3 256 = 4^4 Step 3: Relate the input values to the exponents. We need a rule y = 4^exponent where the exponent depends on x. If the exponent is x-1: For x = 2, exponent is 2-1 = 1, so y = 4^1 = 4. For x = 3, exponent is 3-1 = 2, so y = 4^2 = 16. For x = 4, exponent is 4-1 = 3, so y = 4^3 = 64. For x = 5, exponent is 5-1 = 4, so y = 4^4 = 256. This pattern matches all the given values. Step 4: Select the correct rule from the options. The rule that fits the mapping is y = 4^x-1. Comparing this with the given options: A. y = 4x - 1 B. y = 2x - 1 C. y = 4^x-1 D. y = 4^x The correct option is C. The final answer is C. y = 4^x-1. Send me the next one 📸