Solve each of the following logarithmic equations.
1.The value of a machine is$450 000 and its value depreciates by 20% every
year.At least how many years later will its value be less than$100 000?
ANS:7 years
2. Mr. chan borrows $10 000 from a bank at an interest rate of 12% p.a.
compounded monthly.For at most how many months can Mr. chan borrow
the money so that the total repayment to the bank will not exceed $11 000?
ANS:9 months
F.4 MATHS (log)
2010-03-06 6:16 pm
回答 (1)
2010-03-06 6:25 pm
✔ 最佳答案
(1) Depreciation factor = 0.8 each year, so suppose that n years later its value will be less than $100 000, then450000 x 0.8n < 100000
0.8n < 2/9
n log 0.8 < log (2/9)
n > 6.74 (since log 0.8 < 0)
So 7 years later.
(2) 10000 x 1.01n <= 11000
1.01n <= 1.1
n log 1.01 <= log 1.1
n <= 9.58
So at most can borrow 9 months.
參考: Myself
收錄日期: 2021-04-23 18:26:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100306000051KK00345