(a) Explanation Given: The percent of the public that is aware of new product for tanning is approximated by A ( t ) = 10 t 2 2 − t , where t is the time in months. Calculation: Consider the function A ( t ) = 10 t 2 2 − t (1) Evaluate the derivative of equation (1) as follows. A ′ ( t ) = 10 t 2 ( ln 2 ) 2 − t ( − 1 ) + 20 t ( 2 − t ) A ′ ( t ) = 10 t 2 − t ( − t ln 2 + 2 ) (2) Substitute t = 2 in equation (2) as follows (b) To determine To find: The rate of change of the percent of the public that is aware the product after 4 months. (c) To determine To explain: The reason of public awareness of the product has changed by comparing part (a) and part (b).

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ISBN: 2818440028625

Author: Lial

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Chapter 4.4, Problem 42E

(a)

To determine

To find: The rate of change of the percent of the public that is aware of the product after 2 months.

(b)

To determine

To find: The rate of change of the percent of the public that is aware the product after 4 months.

(c)

To determine

To explain: The reason of public awareness of the product has changed by comparing part (a) and part (b).

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Chapter 4.4, Problem 41E

Chapter 4.4, Problem 43E

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