1)A durable trye manufacturer claims the tyre produced Has the following rlations
P = 100(2^(-0.000 5m))
where P is its remaining life-span (expressed as a percentage), m is the number of kilometers it travelled
A) Find the remaining life-span ( a percentage) of tyre after travelling 4000 km
B)For safely, when the remaining life-span of the tyre is less than 5%, such tyre should be replaced. If thje tyres of a car has travelled 9 000 km, should they be replaced?
C)(i) Make m the subject of the given formula
(ii) If a tyre has only half its life-span remained, find the distance in kilometers that the tyre has travelled
2)A direct selling company has now 30 customers, each has an average monthly expenditure of $240. Suppose the number of customers increases by 30% every month and the average monthly expenditure of each customer increase by 10% every month. Let the number of customers, the average monthly expenditure of each customer and the monthly sales of the company after n month be x, $y and $C respectively
.
A)Express x, y and C in terms of n
B)Find the monthly sales of the company after 6 months.
C)At least how many month later will be monthly sales of the company be more than $1 000 000? what are the number of the customers and the average monthly expenditure of each customer then? (Given the answers correct to the nearest integer if necessary)
F4 Maths
2012-07-21 6:27 pm
回答 (1)
2012-07-21 6:40 pm
✔ 最佳答案
1(a) P = 100(2^(-0.0005 * 4000)) = 25(b) P = 100(2^(-0.0005 * 9000)) = 4.4194Since 4.4194 < 5, the tyre should be replaced(c)(i) P = 100(2^(-0.0005m))2^(-0.0005m) = P/100(-0.0005m)log 2 = log(P/100)m = log(P/100)/(-0.0005log2)m = -2000log(P/100)/log2...(*)(ii) Sub. P = 50 into *m = -2000log(50/100)/log2 = 2000 The tyre has travelled 2000 km2(a) x = 30(1 + 30%)^n = 300(1.3)^n, y = 240(1 + 10%)^n = 240(1.1)^nC = 30(1 + 30%)^n * 240(1 + 10%)^n = 7200(1.43)^n(b) sub. n = 6C = 7200(1.43)^6 = 61567.10337(c) Let C = 7200(1.43)^n > 1000000(1.43)^n > 138.8889n log1.43 > log 138.8889n > 13.7938So, after 14 months, the monthly sales of the company will be more than
$1 000 000. The no. of customer is 300(1.3)^14 = 11812The average monthly expenditure of each customer = 911
收錄日期: 2021-04-27 17:46:03
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