To determine how many pieces of candy the store will sell in 25 years, we first need to understand the growth of the candy sales. According to the problem, the candy sales triple every 6 years.
First, we calculate how many 6-year periods there are in 25 years:
\[ \frac{25 \text{ years}}{6 \text{ years/period}} \approx 4.167 \text{ periods} \]
We can take the integer part (4 complete periods), which means we will be observing 4 complete cycles of tripling.
Now, we calculate how many total candies the store will sell after these 4 periods.
Initially, the store sells 1,567,401 pieces of candy. After each 6-year period, the sales will triple:
\[ \text{After 1 period: } 1,567,401 \times 3 \] \[ \text{After 2 periods: } (1,567,401 \times 3) \times 3 = 1,567,401 \times 3^2 \] \[ \text{After 3 periods: } (1,567,401 \times 3^2) \times 3 = 1,567,401 \times 3^3 \] \[ \text{After 4 periods: } (1,567,401 \times 3^3) \times 3 = 1,567,401 \times 3^4 \]
Now we compute \(3^4\):
\[ 3^4 = 81 \]
So, after 4 periods, the number of candies sold will be:
\[ 1,567,401 \times 81 \]
Now, we perform the multiplication:
\[ 1,567,401 \times 81 = 127,876,481 \]
So, the store will sell 127,876,481 pieces of candy in 25 years.
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