National Health expenditures per capita (in dollars) have risen dramatically in recent years. By using data from the centers for Medicare and Medicaid Services from 2016 and projected to 2021, the rate of change of health expenditures per capita can be modeled by fraction numerator d E over denominator d t end fraction equals 41.22 t space minus space 116.4 dollars per year where t is the number of years past 2000. If these expenditures were $9808 in 2014, find the predicted national health expenditures per capita in 2020. Round answer off to the nearest penny.

Question

Mathematics

Leia

5 March, 06:09

National Health expenditures per capita (in dollars) have risen dramatically in recent years. By using data from the centers for Medicare and Medicaid Services from 2016 and projected to 2021, the rate of change of health expenditures per capita can be modeled by fraction numerator d E over denominator d t end fraction equals 41.22 t space minus space 116.4 dollars per year where t is the number of years past 2000. If these expenditures were $9808 in 2014, find the predicted national health expenditures per capita in 2020. Round answer off to the nearest penny.

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Answers (1)

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Hayden Lowe · Answer 1

The predicted national health expenditures per capital in 2020 is 13314.04

Step-by-step explanation:

Solution

Given that,

de/dt = 41.22t - 116.4

⇒∫dt = ∫ (41.22t - 116.4) dt

E = 20.61 t² - 116.4 e + c

But at e (14) = E becomes = 98.08

⇒9808 = 20.61 (14) ² - 116.4 (ln) + c = 7348.04

Then,

E = 20.61 t² - 116.4 (t) + 7348.04

Thus in 2020,

t = 20

E = 20.61 (20) ² - 116.4 (2) ² + 7348.04

= 13314.04