   Chapter 11, Problem 16T ### 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

# By using U.S. Centers for Medicare and Medicaid Services data from 2000 and projected to 2018, the total U.S. expenditures (in billions of dollars) for health services and supplies can be modeled by y = 1319 e 0.062 t where t = 0 in 2000.(a) Find the function that models the rate of change.(b) Find the model’s value for the rate of change of U.S. expenditures for health services and supplies in 2005 and in 2020.

(a)

To determine

To calculate: The rate of change of the function that is modelled by the equation y=1319e0.062t, where, t is the number of years after 2000 if using U.S. Centers for Medicare and Medicaid services data from 2000 and projected to 2018, the total U.S. expenditure in billions for professional services and retail medical products is given as above.

Explanation

Given Information:

The provided expression is y=1319e0.062t,

Where, t is the number of years after 2000.

Formula Used:

As per the product rule, if two functions are given in the form [f(x)g(x)], then the derivative is given as:

ddx(fg)=[fdgdx+gdfdx]

If p=f(q) is the demand for the q units and price p, then at the points (qA,pA), then,

Rate is the first derivative of the equation.

Calculation:

Consider the provided expression,

y=1319e0

(b)

To determine

To calculate: The models value for the rate of change in 2005 and 2020 by the equation given as y=1319e0.062t, where, t is the number of years after 2000. If the U.S. Centers for Medicare and Medicaid services data from 2000 and projected to 2018, the total U.S. expenditure in billions for professional services and retail medical products is provided as above.

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