Question

DUE ASAP

'7. Health Expenditures: National Health Expenditures per capita ($) have risen dramatically since the year 2000. The rate of change of health expenditures per capita can be modeled as follows: dE/dt = 2.73t^2 - 50.6t +549 Where: t = the # of years past 2000 E(t) = Health expenditures per capita ($) a. Find the function (E(t) that models the National Health Expenditure per capita if these expenditures were $8428 in 2000.1 b. Predict the national health expenditure per capita for 2020. *

Answer 1

a ] Here, dE = 2.73ť - 50.6t + 549 - 1 I dt where t is no of years past 2000. Now, to find Ect) we will integrate egun E(t) = f d t = S (2 7 3 4² - 50.6E +549) dt ECE) = 2.73 t - so 6 + +549t to where, c is constant or integration Now, we are given that expenditure was $8428 dollars when in 2000. E CO) = 8428 C 2000 is base years hers) E(q) = 2.73 +3 - 50.6 t² +549€ + c = Eco) = 2.73 (0) - 50 6 Col +549 (0) + c -) $428 = C. roo EEE) = 0.91 - 25.3t +54 9 t + 8428 3 )N now, to predict natloncel health expenditore per capire for 2020. For 2020, t=20 - E (20) = o-91 (20) 3 - 25.3 (20) + 549 (20) +8428 = 0.91(8000) - 25.3 (400) + 549 (20) +8428 ارسال I (20) = 7280 - 10120t logso +8420 EC2O) = 16568 . National health expenditure per capita in 2020 is $16568.