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I do not now how to face this problem

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by jfranco23 » Mon Feb 16, 2009 5:18 pm
At the end of each year the value of a certain antique watch is c% more than its value one year earlier, where c has the same value each year. If the value of the watch was k dollars on January1, 1992 and m dollars on January 1, 1994, then in terms of m and k, what was the value of the watch, in dollars, on January1, 1995?

A. m + 1/2(m-k)
B. m + 1/2((m-k)/)m
C. (m(rootm))/rootk
D. m^2/2k
E. k(m^2)
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Re: I do not now how to face this problem

by billzhao » Mon Feb 16, 2009 5:36 pm
jfranco23 wrote:At the end of each year the value of a certain antique watch is c% more than its value one year earlier, where c has the same value each year. If the value of the watch was k dollars on January1, 1992 and m dollars on January 1, 1994, then in terms of m and k, what was the value of the watch, in dollars, on January1, 1995?

A. m + 1/2(m-k)
B. m + 1/2((m-k)/)m
C. (m(rootm))/rootk
D. m^2/2k
E. k(m^2)
To find the value: V of the watch in 1995, we need to find the appreciation rate c% in terms of m or k.

Knowing the value of the watch is k in 1992 and m in 1994, we have:
m=k(1+c%)^2 =>
(1+c%)^2=m/k =>

1+c%=root(m/k)

V=m(1+c%)=m*root(m/k)=(m(rootm)/rootk

Answer is (C)
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