An overseas Filipino workers in the Budget Department is Saudi Arabia. He found out that the cost C, in US dollars, of repairing a city street in that country was estimated using the function:
C(m)=2,000+6,000m
where m is the number of miles of street to be repaired.
a. graph of the function for 0(less than or equal to)m(less than or equal to)10.
b.Estimate the cost of repairing 7 miles of a city street
c.How many miles of city street would have been repaired if the Budget Department had allotted $50,000?
THANK YOU :))
12
Draw the graph of the function for 0 ≤ m ≤ 10
a. To graph the function C(m) = 2,000 + 6,000m, we need to plot points for different values of m within the given range for m.
Let's start by finding the cost for m = 0:
C(0) = 2,000 + 6,000(0) = 2,000
So, when there are 0 miles of street to be repaired, the cost is $2,000.
Now, let's find the cost for m = 1:
C(1) = 2,000 + 6,000(1) = 8,000
So, when there is 1 mile of street to be repaired, the cost is $8,000.
We can continue to find the cost for other values of m and plot the points on a graph. For simplicity, let's use increments of 1 for m within the given range, i.e., m = 2, m = 3, etc. up to m = 10.
Using this approach, we can obtain the following points:
m = 0: (0, 2,000)
m = 1: (1, 8,000)
m = 2: (2, 14,000)
m = 3: (3, 20,000)
m = 4: (4, 26,000)
m = 5: (5, 32,000)
m = 6: (6, 38,000)
m = 7: (7, 44,000)
m = 8: (8, 50,000)
m = 9: (9, 56,000)
m = 10: (10, 62,000)
Plot these points on a Cartesian plane where the x-axis represents m (miles) and the y-axis represents the cost C (USD). Then connect the points with a line, and you will have the graph of the function C(m) = 2,000 + 6,000m for 0 ≤ m ≤ 10.
b. To estimate the cost of repairing 7 miles of a city street, we can substitute m = 7 into the function C(m) = 2,000 + 6,000m.
C(7) = 2,000 + 6,000(7) = 44,000
Therefore, the estimated cost of repairing 7 miles of a city street is $44,000.
c. To find out how many miles of city street would have been repaired if the Budget Department had allotted $50,000, we need to solve the equation C(m) = 2,000 + 6,000m = 50,000.
Rearranging the equation, we have:
6,000m = 50,000 - 2,000
6,000m = 48,000
Dividing both sides by 6,000:
m = 48,000 / 6,000
m = 8
Therefore, if the Budget Department had allotted $50,000, approximately 8 miles of city street would have been repaired.
a) this is simply a straight line with y-intercept of 2000 and a slope of 6000
I would scale my graph so each vertical unit (the y) represents 1000 dollars, and each horizontal unit , the x's, represents the number of miles.
b) think in thousands only.
Can you mentally find 6x7 + 2 and then say "thousand" after it ?
c) solve:
2000 + 6000m = 50000