Value of Computer Software
The value V, in dollars, of a shopkeeper's inventory is software program is given by V=-50t + 300, where t is the number of years since the shopkeeper first bought the program. SHOW YOUR WORK for a and c.
a) Find the value of the software after 0 years, 4 years, and 6 years.
b) Use graph paper to graph the equation and then use the graph to estimate the value of the software after 5 years.
c) After how many years is the value of the software $150?
V = -50t + 300.
a. V = -50*0 + 300 = $300.
V = -50*4 + 300 = $100.
V =
b. The following points maybe used for graphing:
(t,V) = (0,300), (2,200), (4,100),
(6,0).
c. -50t + 300 = 150 Solve for t.
To find the value of the software after a certain number of years, we can substitute the given values of t into the expression V = -50t + 300.
a)
To find the value of the software after 0 years (t = 0):
V = -50(0) + 300
V = 0 + 300
V = 300
So, after 0 years, the value of the software is $300.
To find the value of the software after 4 years (t = 4):
V = -50(4) + 300
V = -200 + 300
V = 100
So, after 4 years, the value of the software is $100.
To find the value of the software after 6 years (t = 6):
V = -50(6) + 300
V = -300 + 300
V = 0
So, after 6 years, the value of the software is $0.
b)
To graph the equation V = -50t + 300, we can plot a graph by assigning the values of t on the x-axis and the corresponding values of V on the y-axis. We can choose a suitable scale for the graph.
The graph will have a downward slope and will intersect the y-axis at 300. The line will continue to extend into the negative x-axis.
To estimate the value of the software after 5 years, we can look at the graph and determine the y-coordinate for x = 5. We can approximate the value from the intersection of the line with x = 5 on the graph.
c)
To find the number of years when the value of the software is $150, we can set V = 150 and solve for t in the equation V = -50t + 300.
150 = -50t + 300
Subtracting 300 from both sides:
-150 = -50t
Dividing by -50:
t = (-150) / (-50)
t = 3
Therefore, the value of the software will be $150 after 3 years.