the cost of renting a kayak for one hour is $23. Each additional hour is 8$ more. Write an explicit formula and recursive formula to represe

Question

the cost of renting a kayak for one hour is $23. Each additional hour is 8$ more. Write an explicit formula and recursive formula to represent the situation.

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Abigail 1 week 2021-10-12T09:04:44+00:00 2 Answers 0

Answers ( )

    0
    2021-10-12T09:05:47+00:00

    Explicit formula a_{n} =8n+15

    Recursive formula \left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.

    To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:

    {23, 31, 39, 47, 55,…..,n}

    Writing a recursive formula of the form a_{n} =a_{n-1} +d where a_{n} is the nth term, n the number of terms, and d the common difference in the secuence.

    The common difference of the secuence {23, 31, 39, 47, 55,…..,n}. So, the first term is a_{1} =23, and the common diffenece is d = 8 which is the difference between each term.

    \left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.

    Writing a explicit formula of the form a_{n} =a_{1} +d(n-1) where where a_{n} is the nth term, n the number of terms, a_{1} the first term of the secuence, and d the common difference in the secuence.

    With a_{1}=23, and d = 8:

    a_{n} =23+8(n-1)

    a_{n} =23+8n-8

    a_{n} =8n+15

    0
    2021-10-12T09:06:27+00:00

    X= 23+8y
    X represents the total
    23 represents the base price
    8 represents the price per extra hour
    Y represents how many hours extra

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