The cost of a pound of grapes from​ Frank's Farmstand is $ 2.25 for the first​ pound, and $ 2.00 for each additional pound. Choose the graph that shows the​ cost, C, in​ dollars, of the grapes as a function of​ weight, w, in​ pounds, on the interval left parenthesis 0 comma 4 right bracket.

Question

Question content area bottom
Part 1
Choose the correct answer​ below:
A.
0
1
2
3
4
5
0.00
5.00
10.00
15.00
w
C(w)

x y graph
B.
0
1
2
3
4
5
0.00
5.00
10.00
15.00
w
C(w)

x y graph
C.
0
1
2
3
4
5
0.00
5.00
10.00
15.00
w
C(w)

x y graph
D.
0
1
2
3
4
5
0.00
5.00
10.00
15.00
w
C(w)

Answer 1

To find the correct graph that represents the cost of grapes as a function of weight, let's break down the pricing structure given:

1. The first pound of grapes costs $2.25.
2. Each additional pound costs $2.00.

So we can summarize the cost, C, for different weights, w:

• For \( w = 1 \): \( C(1) = 2.25 \)
• For \( w = 2 \): \( C(2) = 2.25 + 2.00 = 4.25 \)
• For \( w = 3 \): \( C(3) = 4.25 + 2.00 = 6.25 \)
• For \( w = 4 \): \( C(4) = 6.25 + 2.00 = 8.25 \)

Using this information, we can plot the costs for each weight:

• At \( w = 1 \), \( C = 2.25 \)
• At \( w = 2 \), \( C = 4.25 \)
• At \( w = 3 \), \( C = 6.25 \)
• At \( w = 4 \), \( C = 8.25 \)

Now we can check which graph correctly represents these points:

• The graph should start at \( (0, 0) \) and increase steeply to \( (1, 2.25) \), then continue to increase in a linear manner, hitting \( (2, 4.25) \), \( (3, 6.25) \), and \( (4, 8.25) \).

Without the visual options to refer to, it's difficult to accurately choose one of the graphs directly. However, you should look for a graph that:

• Starts at the origin (0, 0)
• Has a point at (1, 2.25)
• Continues to a point at (2, 4.25)
• Continues to a point at (3, 6.25)
• Ends at (4, 8.25)

Look for the lines or points corresponding to these values in the options provided to make the final choice.