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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. *
math question ?
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.
回答 (2)
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!
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!
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)
(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)
收錄日期: 2021-04-24 08:09:23
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