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29 June, 10:42

The number of liver transplants performed in a particular country in year x is approximated by f left parenthesis x right parenthesisf (x) equals=negative 245.4 plus 2327 ln x-245.4+2327lnx where x greater than or equals 5x≥5 and xequals=5 corresponds to the year 1995. (a) estimate the number of transplants in 20252025. (b) find the rate of change for the number of transplants in 20252025.

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  1. 29 June, 12:57
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    (a). The function is written as: f (x) = - 245.4 + 2327lnx

    First, let's find the number of years between 1995 and 2025.

    Number of years = 2025 - 1995 = 30

    Since x = 5 represents the base year 1995, that mean we have to take x = 35.

    f (35) = - 245.4 + 2327ln (35) = 3,500 transplants by 2025

    (b). The rate of change is determined through differential calculus.

    f' (x) = 2327 (1/x) = 2327/x

    f' (35) = 2327/35 = 66.5

    Thus, the rate of change of transplants is 66.5 per year.
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