for every mile you drive it cost 3.50$ making so 1,3.5 2,7 3,10.5 4,14 5,17.5 6,21 7,24.5 8,28 9,31.5 10,35 for the first ten terms make a formula

Answer 1

To derive a formula for the cost based on the number of miles driven, we can observe the pattern in the costs you've provided.

The cost for driving \( n \) miles is as follows:

• 1 mile: $3.50
• 2 miles: $7.00
• 3 miles: $10.50
• 4 miles: $14.00
• 5 miles: $17.50
• 6 miles: $21.00
• 7 miles: $24.50
• 8 miles: $28.00
• 9 miles: $31.50
• 10 miles: $35.00

From this, we can observe that the cost increases linearly. The formula for the cost \( C \) based on the miles driven \( n \) can be described as:

\[ C(n) = 3.50n \]

where:

• \( C(n) \) is the total cost in dollars,
• \( n \) is the number of miles driven.

To verify, we can plug in the values of \( n \):

• For \( n = 1 \): \( C(1) = 3.50 \times 1 = 3.50 \)
• For \( n = 2 \): \( C(2) = 3.50 \times 2 = 7.00 \)
• For \( n = 3 \): \( C(3) = 3.50 \times 3 = 10.50 \)
• For \( n = 4 \): \( C(4) = 3.50 \times 4 = 14.00 \)
• For \( n = 5 \): \( C(5) = 3.50 \times 5 = 17.50 \)
• For \( n = 6 \): \( C(6) = 3.50 \times 6 = 21.00 \)
• For \( n = 7 \): \( C(7) = 3.50 \times 7 = 24.50 \)
• For \( n = 8 \): \( C(8) = 3.50 \times 8 = 28.00 \)
• For \( n = 9 \): \( C(9) = 3.50 \times 9 = 31.50 \)
• For \( n = 10 \): \( C(10) = 3.50 \times 10 = 35.00 \)

This confirms that the formula \( C(n) = 3.50n \) accurately represents the cost for driving \( n \) miles.