Your elderly neighbor places a bag of rice on your doorstep each morning. The first day, the bag contains 1 grain of rice; the second day, it contains 2 grains of rice; the third day, it contains 4 grains of rice, and so on, doubling each day. Each grain of rice weighs 0.03 grams. How much will the contents of the bag weigh on the 25th day? Round your answer to the nearest hundredth, if necessary.

Question

29-05-2025
Mathematics

High School

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Your elderly neighbor places a bag of rice on your doorstep each morning. The first day, the bag contains 1 grain of rice; the second day, it contains 2 grains of rice; the third day, it contains 4 grains of rice, and so on, doubling each day. Each grain of rice weighs 0.03 grams. How much will the contents of the bag weigh on the 25th day? Round your answer to the nearest hundredth, if necessary.

Answer :

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ishuraj00008 ishuraj00008 · Answer 1 · 2023-08-13T22:42:41-04:00

Final answer:

The bag of rice on the 25th day will weigh approximately 50331648 grams (or 50331.648 kilograms), assuming the number of rice grains increases by doubling each day.

Explanation:

The question seems to be based on the concept of geometric progression, where the neighbor's bag of rice increases its quantity by doubling each day. On the first day, the bag had 1 grain of rice, on the second day it had 2, on the third day it had 4, and so on. Therefore, the number of rice grains on a given day would be 2n-1 where n is the number of the day.

To find how much the bag of rice will weigh on the 25th day, first, we calculate the number of grains on the 25th day, which will be 225-1 = 224 grains. Then, we multiply this number by the weight of each grain of rice: 224 * 0.03g = 50331648 grams. Thus, the bag will weigh approximately 50331648 grams (or roughly 50331.648 kilograms) on the 25th day. Remember that the grain count is based on the assumption of geometric progression.

Learn more about Geometric Progression here:

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