buckkitty wrote:
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 January 1, 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)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2
For an algebraic approach, we need to recognize that the value of the watch increases by the same factor each year. So, for the ease of calculations, let's say that the value increases by a factor of F.
Aside: Notice that the answer choices do not include the variable c. This tells me that I don't need to keep that variable in my solution.
In 1992, the watch is valued at k dollars.
In 1993, the watch is valued at kF dollars (applying our constant increase of F)
In
1994, the watch is valued at
kF² dollars
In 1995, the watch is valued at kF³ dollars
GREAT, we now know the value in 1995. However, when we check the answer choices, none match the expression kF³. So, we have some more work to do.
The question tells us that, in
1994, the watch is valued at
m dollars.
So, we now know that
kF² = m.
Let's solve this equation for F (you'll see why in a moment)
We get: F² = m/k
F = √(m/k)We can rewrite this as:
F = (√m)/(√k)We know that the
1995 value = kF³ dollars.
Rewrite, to get the 1995 value = (
kF²)(
F)
If we replace
kF² with
m and replace
F with
(√m)/(√k), we get:
1995 value = (
m)(
(√m)/(√k))
= (m√m)/(√k)
= C
Cheers,
Brent