Arithmetic and Geometric Sequ.

Tieria

2009-11-29 7:36 am

1. There are many lotuses grown in a pond. Suppose the lotus leaves continue to grow such that the area they cover the pond doubles every day. If the lotus leaves will cover the whole pond after ten days, after how many days will cover one quarter of the pond?

The answer is 8 days.

2. The gross product of a certain company in the year 2003 is 11 million dollars. It is projected that the gross product will increase steadily every year by 6%.

(a) Find the gross product of the company in 2010, correct to 3 significant figures.
(b) In which year will the gross product of the company just exceed twice the gross product in 2003?

The answers are (a) 16.5 million dollars and (b) 2015.

回答 (1)

用戶9112

2009-11-29 8:05 am

✔ 最佳答案

1. Let the current coverage = x
In ten days time the coverage will be x * 2^10 = 100%
x = 2^(-10)
In coverage at nth day = 2^(-10)*2^n = 2^(n - 10)
When 2^(n - 10) = 1/4 = 2^(-2) => n = 8
The answer is 8 days.
2. (a) The gross product of the company in 2010 = 11 million * (1 + 6%)^7
= 11 * 1.06^7
= 16.5 million dollars
(b) 11 million * (1 + 6%)^n > 22 million
1.06^n > 2
nlog(1.06) > log2
n > log2/log(1.06) = 11.89
n should be 12 years so 2003 + 12 = 2015
In 2015 the gross product of the company will just exceed twice the gross product in 2003

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