Question

四道用英语写的数学题，给50分！

1.Jason spends 20 minutes on the internet the first day the new computer arrives.
Each day he increases the time spent on the internet by 7% from the day before.
What is the total time Jason has spent on the internet in the first 21 days

2.Jason buys a laptop computer for 4800dollars

The computer depreciates at the rate of 32% per year,to the nearest year,will it take for the laptop to reduce to one-tenth of its original value?

3.Aunt Jane helps Jason with his savings.
In week 1 she gives him 75 dollars.
Each week she reduces the amount she gives him by 20% of the previous week's amount.

If this continues indefinitely,how much will Aunt Jane give Jason in total?

4.Jeremy decides to reduce his internet ues by the same number of minutes each week.
Jeremy uses the internet for 1490minutes in week 9,and the total number of minutes of his internet use after 24 weeks is 29880 minutes.
For how many minutes did Jeremy use the internet in week 1 of his Reduction Plan?

Answer 1

我就不用英文给你解了。看来出题者想考考你等比数列啊，不知道你学没学。
1.第1天，用20分钟，
第2天，用了（20+20×7%）=20×（1+7%）=A2
第3天，用了(A2+A2×7%）=A2(1+7%)=20(1+7%)的平方=20(1+7%)^2
以此类推，第二十天用了20(1+7%)^19.所以根据等比数列求和公式，首项是20
，公比是（1+7%），总共用的时间为s=20[（1+7%）^20-1]/[(1+7%)-1]结果就自己算吧。
2第一年，给了4800$
第二年，给了(4800-4800×32%）=4800（1-32%）。
第三年，给了4800（1-32%）^2,和第一题一样，接下来的两道题我就不解释了。
他问，电脑能否就到原来价钱的十分之一，设降到原来价钱的十分之一，需要n年。所以4800（1-32%）^n=4800/10,利用求对数方法看n是否为整数。最后求解出来n不存在。
3.第一周，给了75$
第二周，给了75(1-20%)
第三周，给了75(1-20%)^2
他说要无限期的按这种方式给钱。杰森总共弄收到多少钱
设给了n天的钱所以第n周，给了75(1-20%)^（n-1）
所以总共给了s=75[(0.8)^n-1]/(0.8-1)
0.8<1,一个小于一的数无限的乘以它本身就无限的接近于0，所以0.8^n=0
所以s=75/(1-0.8)=375
4 这道题是等差数列，设第一周上网时间为A1,每周介绍的上网时间为d
所以第一周用了A1
第二周用了（A1-d）=A2
第三周用了（A1-2d）

第九周用了(A1-8d)
前九周用的时间s=(2A1-8d)×9/2=1490
前33周用时间s=（2A1-32d）×33/2=29880,求出A1和d，
即为his Reduction Plan

Answer 2

1: 20乘以7%乘以7%……(20个)=

Answer 3

靠！太变态！~

Answer 4

khodkg[rkgofd