Maths question

👨🏻‍🏫 學術台數學

用戶109355

2006-11-12 2:03 am

In a estate, the population in the first is 10250 and it increases to 11480 in the second year. It is estimated that the population will increase at the same rate for the next few years.The community services for the aged in the estate are expected to serve 2500 old people in the first year. The number of old people who will receive these services is expected to increase at a stesdy rate of 10% per year.

更新1:

It is estimated that in the seventh year, 34% of the population in the estate will be old people.Will there be sufficient community services provided for the aged by that time? Please show the steps and explain

回答 (2)

用戶3640

2006-11-12 2:14 am

✔ 最佳答案

%increase in population /yrs=(11480-10250)/10250x100%
=12%

no. of old people in the 7th yrs=10250(1+12%)^6x34%
=6879,cor. to the nearest whole no.

no. of old people receiving service in 7th yrs=2500(1+10%)^6=4429,cor. to the nearest whole no.

since 4429 is less than 6879

so there isn'e sufficient community services provided

參考: me

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chuszeching

2006-11-12 2:28 am

First, you have to find the growth rate of the population.

(11480 - 10250)/ 10250 x 100% = 12%

Then u can use the growth rate to find the population in the seventh year.
i.e. 10250 * (1+12%) to the power 7~ (similar to the calculation to find the compounded interest)

After u find the population in 7th year, then u times 34% with that amount, then u can know how many old people in the 7th year. (answer A)

Second part, u have to find the service provided in the 7th year.
2500 * ( 1 + 10%) to the power 7~ (answer B)

Then u can compare answers A and B to see whether it is sufficient. (A > B -- insufficient; A < B -- sufficient)

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