The resale value V, in thousands of dollars, of a boat is a function of the number of years t since the start of 2011, and the formula is

Question

The resale value V, in thousands of dollars, of a boat is a function of the number of years t since the start of 2011, and the formula is
V = 12.5 − 1.3t.
(a) Calculate V(3).
(b) In what year will the resale value be 7.3 thousand dollars?
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
(d) In what year will the resale value be 3.4 thousand dollars?

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Cherry 2 months 2021-08-19T04:51:28+00:00 1 Answers 5 views 0

Answers ( )

    0
    2021-08-19T04:52:55+00:00

    Answer:

    a) V(3) = 8.6.

    b) The resale value will be 7.3 thousand dollars at the start of 2015.

    c) t(V) = \frac{12.5 - V}{1.3}

    d) 2017

    Step-by-step explanation:

    We are given the following function:

    V(t) = 12.5 - 1.3t

    (a) Calculate V(3).

    This is V when t = 3. So

    V(3) = 12.5 - 1.3(3) = 8.6

    So

    V(3) = 8.6.

    (b) In what year will the resale value be 7.3 thousand dollars?

    t years after the start of 2011, and t is found when V(t) = 7.3. So

    V(t) = 12.5 - 1.3t

    7.3 = 12.5 - 1.3t

    1.3t = 5.2

    t = \frac{5.2}{1.3}

    t = 4

    2011 + 4 = 2015

    The resale value will be 7.3 thousand dollars at the start of 2015.

    (c) Solve for t in the formula above to obtain a formula expressing t as a function of V.

    V(t) = 12.5 - 1.3t

    1.3t(V) = 12.5 - V

    t(V) = \frac{12.5 - V}{1.3}

    (d) In what year will the resale value be 3.4 thousand dollars?

    t years after 2011, and t is found t when V = 3.4. So

    V(t) = 12.5 - 1.3t

    3.9 = 12.5 - 1.3t

    1.3t = 8.6

    t = \frac{8.6}{1.3}

    t = 6.62

    2011 + 6.62 = 2017

    So the year is 2017.

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