SOLUTION: The book value of a machine is expressed by the equation V = 60,000 - 7,500 t
Where V equals the book value in dollars and t equals the age of the machine expressed in years.
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Question 1183143: The book value of a machine is expressed by the equation V = 60,000 - 7,500 t
Where V equals the book value in dollars and t equals the age of the machine expressed in years.
(a) Identify the t and V intercepts.
(b) Interpret the meaning of the intercepts.
(c) Interpret the meaning of the slope.
(d) Sketch the function.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
v = 60,000 - 7500 * t
v = the book value.
t = the age of the machine in years.
to find the t-intercept, set v = 0 and solve for t.
you will get:
0 = 60,000 - 7500 * t
add 7500 * t to both sides of the equation to get:
7500 * t = 60,000
solve for t to get:
t = 60,000 / 7500 = 8
to find the v-intercept, set t = 0 and solve for v.
you will get:
v = 60,000
the t-intercept is the value of t when v = 0.
since v represents the book value of the machine, the t-intercept tells you when the book value of the machine is 0.
the v-intercept is the value of v when t = 0.
since t is the age of the machine in years, the v-intercept tells you the value of the machine when it is new.
to graph the equation, set y equal to v and x equal to t.
the graph looks like this:
the format of the equation is y = mx + b
m is the slope
b is the y-intercept.
replace y with v and x with t and the equation becomes:
v = mt + b
what you were shown is v = b + mt
that became v = 60,000 - 7500 * t
re-order the terms to get:
v = -7500 * t + 60,000
that shows that -7500 is the slope and 60,000 is the v-intercept
for graphing purposes, y takes the place of v and x takes the place of t.
-7500 is the slope.
the slope is the change in y divided by the change in x.
in this equation, the slope is telling you that the book value of the machine is reduced by 7500 each year.
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