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by ketkoag » Sat Mar 28, 2009 3:18 am
At the end of each year, the value of a certain antique watch is c percent 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 January 1, 1995 ?

A. m + (1/2)(m – k)
B. m + 1/2(m -k)m/k
C. m^(3/2)/k^.5
D. m^2/(2k)
E. km^2

OA: C
I got this answer correctly, yet lemme know how to solve it without assuming the values for each variable and comparing with the answer choices.
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by DanaJ » Sat Mar 28, 2009 3:28 am
The watch's value increases by c percent each year. This means that, if we consider the initial value x, then the following year its value will be x*(100 + c)%. In order to make the explanation shorter, let's use the following notation:
(100 + c)% = C.

Now you get:

value in 1992: k
value in 1993: k*C
value in 1994: k*C*C = k*C^2 = m
value in 1995: k*C*C*C = k*C^3 - in order to express this by using k and m, we need to express C using k and m. This is why we'll use the value for 1994:
k*C^2 = m
C^2 = m/k
C = sqrt(m/k).

This in turn will make the value for 1995 k*[sqrt(m/k)]^3 = k * [m^(3/2)]/[k^(3/2)] = k * m^(3/2) * k^(-3/2) = m^(3/2) * k^(1 - 3/2) = m^(3/2)*k^(-1/2)
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