Question

The number of liver transplants performed in a particular country in year x is approximated by f (x )equalsnegative 239.7 plus 2390 ln x where x greater than or equals 5 and xequals5 corresponds to the year 1995. ​a) Estimate the number of transplants in 2013. ​b) Find f prime (23 ).

Answer 1

a) 7265

b) 103.913

Explanation:

Given the number of liver transplants performed in a particular country in year x approximated by f (x) = -239.7+ 2390lnx where x≥5. If x = 5 corresponds to year 1995. x will be equivalent to 23 in the year 2013.

a) Number of transplant in 2013 can be gotten by substituting x = 18 into the equation above.

f (x) = -239.7+ 2390lnx

f (23) = -239.7+ 2390ln 23

f (23) = -239.7+ 2390(3.14)

f(23) = 7264.9

The number of liver transplant in 2013 is approximately 7265

b) If f (x) = -239.7+ 2390lnx

f'(x) = 2390 * 1/x

f'(23) = 2390/23

f'(23) = 103.913