Math

QuestionA cab driver charges \4permile.Themetershows$7.50for2miles,$11for3miles.Findfaresfor4,5,6miles.4 per mile. The meter shows \$7.50 for 2 miles, \$11 for 3 miles. Find fares for 4, 5, 6 miles. f(4)= f(4)= f(5)= f(5)= f(6)= f(6)= $ Also, write a recursive rule for this fare structure.

Studdy Solution

STEP 1

Assumptions1. The fare for1 mile is 4.Thefareformilesis4. The fare for miles is 7.503. The fare for3 miles is $114. The fare increases in an arithmetic sequence

STEP 2

First, we need to find the common difference in the arithmetic sequence. We can do this by subtracting the fare for1 mile from the fare for2 miles.
d=Farefor2milesFarefor1miled = Fare\, for\,2\, miles - Fare\, for\,1\, mile

STEP 3

Now, plug in the given values for the fare for1 mile and the fare for2 miles to calculate the common difference.
d=$7.50$d = \$7.50 - \$

STEP 4

Calculate the common difference.
d=$7.50$4=$3.50d = \$7.50 - \$4 = \$3.50

STEP 5

Now that we have the common difference, we can find the fare for4 miles,5 miles, and miles. The fare for each mile can be found by adding the common difference to the fare for the previous mile.
f(n)=f(n1)+df(n) = f(n-1) + d

STEP 6

Plug in the values for the fare for3 miles and the common difference to calculate the fare for4 miles.
f(4)=f(3)+df(4) = f(3) + df(4)=$11+$3.50f(4) = \$11 + \$3.50

STEP 7

Calculate the fare for4 miles.
f(4)=$11+$3.50=$14.50f(4) = \$11 + \$3.50 = \$14.50

STEP 8

Plug in the values for the fare for4 miles and the common difference to calculate the fare for5 miles.
f(5)=f(4)+df(5) = f(4) + df(5)=$14.50+$3.50f(5) = \$14.50 + \$3.50

STEP 9

Calculate the fare for5 miles.
f(5)=$14.50+$3.50=$18f(5) = \$14.50 + \$3.50 = \$18

STEP 10

Plug in the values for the fare for5 miles and the common difference to calculate the fare for6 miles.
f(6)=f(5)+df(6) = f(5) + df(6)=$18+$3.50f(6) = \$18 + \$3.50

STEP 11

Calculate the fare for6 miles.
f(6)=$18+$3.50=$21.50f(6) = \$18 + \$3.50 = \$21.50The meter will display 14.50for4miles,14.50 for4 miles, 18 for5 miles, and $21.50 for6 miles.

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