SOLUTION: At a certain rate of compound interest,1 will increase to 2 in a years,2 will increase to 3 in b years, and 3 will increase to 15 in c years .If 6 will increase to 10 in n years ,f

Algebra ->  Probability-and-statistics -> SOLUTION: At a certain rate of compound interest,1 will increase to 2 in a years,2 will increase to 3 in b years, and 3 will increase to 15 in c years .If 6 will increase to 10 in n years ,f      Log On


   

Question 1198173: At a certain rate of compound interest,1 will increase to 2 in a years,2 will increase to 3 in b years, and 3 will increase to 15 in c years .If 6 will increase to 10 in n years ,find the expression for n in terms of a,b and c ( Hint: form equations then use natural logs)
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The given information tells us this:

1%28%281%2Br%29%5Ea%29=2 [1]
2%28%281%2Br%29%5Eb%29=3 [2]
3%28%281%2Br%29%5Ec%29=15 [3]

We are to find n in terms of a, b, and c, given that

6%28%281%2Br%29%5En%29=10 [4]

Solve [4] for n:

%281%2Br%29%5En=10%2F6=5%2F3
n%2Aln%281%2Br%29=ln%285%2F3%29
n=ln%285%2F3%29%2Fln%281%2Br%29 [5]

Similarly solve [1], [2], and [3] for a, b, and c:

%281%2Br%29%5Ea=2
a%2Aln%281%2Br%29=ln%282%29
a=ln%282%29%2Fln%281%2Br%29 [6]

2%281%2Br%29%5Eb=3
b%2Aln%281%2Br%29=ln%283%2F2%29
b=ln%283%2F2%29%2Fln%281%2Br%29 [7]

3%281%2Br%29%5Ec=15
c%2Aln%281%2Br%29=ln%285%29
c=ln%285%29%2Fln%281%2Br%29 [8]

Now look at [5] again....



Then use [6], [7], and [8]...



ANSWER: n = c-b-a