The value of a rare painting has increased each year since it was found at a garage sale. The value of the painting is modeled by the functi

Question

The value of a rare painting has increased each year since it was found at a garage sale. The value of the painting is modeled by the function f(x) = 799(1.03). What
does the 799 represent? What will the painting be worth after 5 years? Round your answer to the nearest dollar.

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Melanie 3 days 2021-10-11T00:02:03+00:00 1 Answer 0

Answers ( )

    0
    2021-10-11T00:03:44+00:00

    799 represents the initial value of the painting

    The painting will be worth $926 after 5 years to the nearest dollar

    Step-by-step explanation:

    The form of the exponential function is f(x)=a(b)^{x} , where

    • a is the initial value ⇒ (at x = 0)
    • b is the growth/decay factor ⇒ (rate of change)
    • If b > 1, then the function is growth ⇒ (increasing)
    • If 0 < b < 1, then the function is decay ⇒ (decreasing)

    The value of a rare painting has increased each year since it was

    found at a garage sale

    The value of the painting is modeled by the function f(x)=799(1.03)^{x}

    We need to know what 799 represents and what the painting will

    be worth after 5 years

    f(x)=799(1.03)^{x}

    ∵ The form of the function is f(x)=a(b)^{x}

    – By comparing the two forms

    ∴ a = 799 and b = 1.03

    ∵ a is the initial value at x = 0

    799 represents the initial value of the painting

    ∵ x represents the number of years

    ∴ x = 5

    – Substitute the value of x in the function by 5

    f(5)=799(1.03)^{5}

    ∴ f(x) = 926.26

    The painting will be worth $926 after 5 years to the nearest dollar

    799 represents the initial value of the painting

    The painting will be worth $926 after 5 years to the nearest dollar

    Learn more:

    You can learn more about the functions in brainly.com/question/10382470

    #LearnwithBrainly

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