   Chapter 2, Problem 53RE

Chapter
Section
Textbook Problem

Testosterone Use Fueled by the promotion of testosterone as an antiaging elixir, use of the hormone by middle-age and older men grew dramatically. The total number of prescriptions for testosterone from 1999 through 2002 is given byN(t) = −35.8t3 + 202t2 + 87.8t +648 (0 ≤ t ≤ 3)where N(t) is measured in thousands and t is measured in years, with t = 0 corresponding to the beginning of 1999. Find the total number of prescriptions for testosterone in 1999, 2000, 2001, and 2002.Source: IMS Health.

To determine

To find: The total number of prescription for testosterone in 1999, 2000, 2001 and 2002.

Explanation

Given:

The total number of prescription for testosterone from 1999 through 2002 is,

N(t)=35.8t3+202t2+87.8t+648(0t3)

Where N(t) measured in thousand and t measured in year and the corresponding year is 1999.

Calculation:

The total number of prescription for testosterone from 1999 through 2002 is,

N(t)=35.8t3+202t2+87.8t+648 (1)

Substitute 0 for t in the equation (1),

N(0)=35.8×03+202×02+87.8×0+648=0+0+0+648=648

The total number of prescription for testosterone (in thousands) in 1999,

N(0)=648Thousands=648,000

Thus, the total number of prescription for testosterone in 1999 is 648,000 .

Substitute 1 for t in the equation (1),

N(1)=35.8×13+202×12+87.8×1+648=35.8+202+87.8+648=902

The total number of prescription for testosterone (in thousands) in 2000 is,

N(1)=902Thousands=902,000

Thus, the total number of prescription for testosterone in 2000 is 902,000

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