To solve this problem, we'll determine how many times larger the diameter of the peach became after James watered it with the magical solution.
1. Initial Diameter: The initial diameter of the peach was [tex]\( 98 \)[/tex] mm.
2. Final Diameter: After watering, the diameter grew to [tex]\( 188,869 \)[/tex] mm.
Let's calculate the growth factor, which is the ratio of the final diameter to the initial diameter:
[tex]\[
\text{Growth Factor} = \frac{\text{Final Diameter}}{\text{Initial Diameter}} = \frac{188,869 \text{ mm}}{98 \text{ mm}}
\][/tex]
When we compute this ratio, we find:
[tex]\[
\text{Growth Factor} \approx 1927.234693877551
\][/tex]
Now let's compare this growth factor to the given choices to determine which one is the closest:
- (A) [tex]\( 2 \cdot 10^3 = 2000 \)[/tex]
- (B) [tex]\( 9 \cdot 10^3 = 9000 \)[/tex]
- (C) [tex]\( 2 \cdot 10^4 = 20000 \)[/tex]
- (D) [tex]\( 9 \cdot 10^4 = 90000 \)[/tex]
The growth factor we calculated is approximately [tex]\( 1927.23 \)[/tex]. Among the choices, the closest value is:
[tex]\[
2 \cdot 10^3 = 2000
\][/tex]
Thus, the closest choice is within a small range from [tex]\( 1927.23 \)[/tex].
Therefore, the answer is:
(A) [tex]\( 2 \cdot 10^3 \)[/tex]
