The Correct Answer and Explanation is:
1.343
To find the value of y, we must evaluate the given summation. The expression is y = Σ_{x=1}^{4} 0.609^x. The sigma notation (Σ) signifies that we need to sum a sequence of terms. The expression to be summed is 0.609^x, and the variable x takes on integer values from the lower limit, 1, to the upper limit, 4.
First, we can expand the summation by writing out each term explicitly for x = 1, 2, 3, and 4:
y = (0.609)¹ + (0.609)² + (0.609)³ + (0.609)⁴
Next, we calculate the value of each individual term:
- For x = 1: 0.609¹ = 0.609
- For x = 2: 0.609² = 0.370881
- For x = 3: 0.609³ ≈ 0.2258665
- For x = 4: 0.609⁴ ≈ 0.1375527
Now, we add these values together to find the total sum, which is the value of y:
y = 0.609 + 0.370881 + 0.2258665 + 0.1375527
y ≈ 1.3433002
The problem requires the answer to be rounded to the nearest thousandth. The thousandth is the third decimal place. To round the value y ≈ 1.3433002, we look at the fourth decimal place, which is 3. Since this digit is less than 5, we round down, meaning we keep the digit in the thousandths place as it is and remove the digits that follow.
Therefore, the value of y rounded to the nearest thousandth is 1.343.
