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.

(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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