math question ?

👨🏻‍🏫 學術台數學

[匿名]

2021-01-18 11:53 pm

Kristy inherited a large fortune from a family member. She plans to give $500,000 of her inheritance to charity. Her plan is to give 1/2, or 2^(-1), to charity in January, and then give half of the remaining amount in February, half again in March and so on.

更新1:

What fraction remains after 6 months? * Write the fraction as a power of 2 with a negative exponent. * What amount is remaining at the end of the year. Round to 2 decimal places. *

回答 (2)

用戶58503

2021-01-19 12:23 am

In Jan, after giving half, she has left 5k/2 = 250000.
In Feb, after giving half, she has left (5k/2)/2 = 5k/(2²) = 125000.
In Mar, after giving half, she has left (5k/(2²))/2 = ...etc

Continue till 6 months, till 1 year.

You can do this, month per month. Show your results here. Then we can go through them with you if need be.

Done!

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Yu Yan

2021-01-19 12:22 am

Fraction given after 6 months = 1/2+1/4+1/8+1/16+1/32+1/64 = 0.5+0.5^2+...+0.5^6
(0.5^7-0.5)/(0.5-1) = 63/64 (Geometric sum)

Fraction remaining after 6 months = 1-63/64 = 1/64 (Complement)

The required fraction as a power of 2 = (1/2)^6 = 2^(-6)

Generalizing, after n months, the remaining fraction = 2^(-n)
At the end of the year, 12 months have passed.
The remaining fraction = 2^(-12).
Thus, the remaining amount = 500, 000 (2^(-12)) = 122.07 (2 dp)

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收錄日期: 2021-04-24 08:09:23
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