   Chapter 13.2, Problem 60E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Health services and supplies expenditures The per capita expenditures for U.S. health services and supplies (in dollars per year) for selected years from 2000 and projected to 2018 can be modeled by H ( t ) =   4676 e 0.053 t where t is the number of years past 2000 (Source: U.S. Centers for Medicare and Medicaid Services). Assuming the model remains valid, evaluate ∫ 20 10 H ( t ) dt and tell what it represents.

To determine

To calculate: The value of 1020H(t)dt and what it represents where the per capita share of U.S. total expenditures for health care is modelled by given by H(t)=4676e0.053t.

Explanation

Given Information:

The provided function is H(t)=4676e0.053t.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral eaxdx=eaxa where a is constant and x is variable.

Calculation:

Consider the function H(t)=4676e0.053t.

Evaluate the integral 1020H(t)dt.

Since, H(t)=4676e0.053t.

Thus, the integral is 10204676e0.053tdt.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Thus, evaluate the integral.

Consider the expression (0.053t).

Differentiate with respect to t.

d(0.053t)dt=0.053d(0

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