1) Mr Chan borrows $10,000 from a bank at an interest rate of 20% 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?
2) In an experiment to investigate the reproduction of a certain kind of cell, it is known that the number(N) of cells at the t-th hour of the experiment can be expressed as the following formula:
N =300 log t
If the number of cells at the t-th hour is increased by 90 when compared with that at 8 hours ago, find the value of t correct to the nearest integer.
ANSWER: 1) 9 years 2)16
F.5 LOG APPLICATION
2010-09-26 12:05 am
回答 (2)
2010-09-26 12:24 am
✔ 最佳答案
1)Suppose Mr Chan can at most borrow money for n months
10,000(1+20%/12)^n<=11,000
(1+1/60)^n<=1.1
log[(1+1/60)^n]<=log1.1
nlog(1+1/60)<=log1.1
n<=log1.1/log(1+1/60)=5.77
Hence, Mr Chan can at most borrow money for 5 months
2)
Denote N to be the new number of cells at t-th hour
N=300logt...(1)
N-90=300log(t-8)...(2)
Sub (1) into (2):
300logt-90=300log(t-8)
300[logt-log(t-8)]=90
logt-log(t-8)=0.3
log[t/(t-8)]=0.3
t/t-8=10^0.3
t=(10^0.3)t-8(10^0.3)
(10^0.3-1)t=8(10^0.3)
t=8(10^0.3)/(10^0.3-1)=16 (corr. to the nearest integer)
2010-09-26 12:45 am
1)
Let x be the months that the total repayment will not exceed $11,000
10,000[1+(20/12)%]^x <=11,000
10,000(1+5/300)^x<=11,000
10,000(305/300)^x<=11,000
(305/300)^x<=11/10
xlog(305/300)<=log(11/10)
x<=5.766
x=5
Ans : 5 months
Let x be the months that the total repayment will not exceed $11,000
10,000[1+(20/12)%]^x <=11,000
10,000(1+5/300)^x<=11,000
10,000(305/300)^x<=11,000
(305/300)^x<=11/10
xlog(305/300)<=log(11/10)
x<=5.766
x=5
Ans : 5 months
收錄日期: 2021-04-16 13:20:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100925000051KK00964