Sequence(ii)

2007-11-01 5:43 am

Suppose the number of visitors to Hong Kong in 2000 was 13 000 000, and thereafter the number of visitors is 5% more than that of the previous year.

(c)Find the total number of visitors to Hong Kong from 20002 to 2047 inclusive.(4 sig fig)

(d)Given that from 1901 to 2099,those can divided by 4 are leap years.(4 sig fig)
(i)Find the number of leap years between 2002 and 2047.
(ii)Find the total amount of visitors to Hong Kong in the leap years between 2002 and 2047.

回答 (1)

abaform

2007-11-01 6:49 am

✔ 最佳答案

c)
The number of visitors to Hong Kong in 2002 is
13000000 * (1 + 5%)^2 = 14332500.
The total number of years to count = 2047 - 2002 + 1 = 46. We set up a geometric sequence with 14332500 as the first term, 1 + 5% = 1.05 as the common ratio, then the answer can be obtained by summing up to the 46th term, i.e.,
sum = 14332500 * (1.05^46 - 1) / (1.05 - 1) = 2417680108

di) Between 2002 and 2047, the first leap year is 2004 and last leap year is 2044.
The number of leap years = (2044 - 2004) / 4 + 1 = 11

ii)
The number of visitors to Hong Kong in 2004 is
13000000 * (1 + 5%)^4 = 15801581.25
We set up a geometric sequence with 15801581.25 as the first term, 1.05^4 as the common ratio, then the answer can be obtained by summing up to the 11th term, i.e.
sum = 15801581.25 * ((1.05^4)^11 - 1) / (1.05^4 - 1) = 554113508 (nearest integer)

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