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James had a peach that was 98mm98\text{mm} in diameter. One day he watered it with a magical solution, and it grew to 188,869mm188,869\text{mm} in diameter. Approximately how many times as large did the diameter of the peach become after James watered it? \newlineChoose 11 answer: \newline(A) 2×1032\times10^{3} \newline(B) 9×1039\times10^{3} \newline(C) 2×1042\times10^{4} \newline(D) 9×1049\times10^{4}

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Q. James had a peach that was 98mm98\text{mm} in diameter. One day he watered it with a magical solution, and it grew to 188,869mm188,869\text{mm} in diameter. Approximately how many times as large did the diameter of the peach become after James watered it? \newlineChoose 11 answer: \newline(A) 2×1032\times10^{3} \newline(B) 9×1039\times10^{3} \newline(C) 2×1042\times10^{4} \newline(D) 9×1049\times10^{4}
  1. Calculate Diameter Increase: Calculate the increase in the diameter of the peach.\newlineOriginal diameter = 98 mm98\,\text{mm}\newlineNew diameter = 188,869 mm188,869\,\text{mm}\newlineIncrease = New diameter - Original diameter\newlineIncrease = 188,869 mm−98 mm188,869\,\text{mm} - 98\,\text{mm}\newlineIncrease = 188,771 mm188,771\,\text{mm}
  2. Determine Times Larger: Determine how many times larger the new diameter is compared to the original diameter.\newlineTimes larger = New diameter / Original diameter\newlineTimes larger = 188,869 mm188,869\,\text{mm} / 98 mm98\,\text{mm}
  3. Perform Division: Perform the division to find the approximate factor of increase.\newlineTimes larger ≈188,86998\approx \frac{188,869}{98}\newlineTimes larger ≈1,927.23\approx 1,927.23
  4. Round Factor of Increase: Round the factor of increase to the nearest power of 1010 to match the answer choices.\newline1,927.231,927.23 is closest to 2,0002,000, which is 2×1032 \times 10^3.
  5. Select Correct Answer: Select the correct answer from the given choices.\newlineThe correct answer is (A) 2×1032\times10^{3}, which is the closest power of 1010 to our calculated value of approximately 1,927.231,927.23.

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