If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the value of f(0), to the nearest hundredth.

Question

If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the
value of f(0), to the nearest hundredth.

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Hồng Cúc 3 years 2021-07-31T15:31:13+00:00 1 Answers 6 views 0

Answers ( )

  1. Ben
    0
    2021-07-31T15:32:22+00:00
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    Given:

    For en exponential function f(a):

    f(-3)=18

    f(1)=59

    To find:

    The value of f(0).

    Solution:

    The general form of an exponential function is:

    f(x)=ab^x          …(i)

    Where, a is the initial value and b is the growth/ decay factor.

    We have, f(-3)=18. Substitute x=-3,f(x)=18 in (i).

    18=ab^{-3}            …(ii)

    We have, f(1)=59. Substitute x=1,f(x)=59 in (i).

    59=ab^{1}            …(iii)

    On dividing (iii) by (ii), we get

    \dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}

    3.278=b^{1-(-3)}

    3.278=b^{4}

    (3.278)^{\frac{1}{4}}=b

    1.346=b

    Substituting the value of b in (iii).

    59=a(1.346)^1

    \dfrac{59}{1.346}=a

    43.83358=a

    a\approx 43.83

    The initial value of the function is 43.83. It means, f(0)=43.83.

    Therefore, the value of f(0) is 43.83.

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