Example 5 A chemical company claims that 6 days after its new insecticide is applied to a one acre field infested with a population of a certain insect, the population will be minimal The company bases its claim on its belief that the function P ( t ) 2 1 3 ( t 5 ) 2 t 1 1 5 , 0 t 2 0 accurately predicts the population size P ( in ten thousands ) of the insect t days after application Assuming the population model is accurate, should the company 's claim be accepted or rejected Solution A figure is not appropriate here The company is making a claim about a function 's maximum value Mathematically, this is a statement about the derivative of the function Since we are given the function, we will differentiate it P ' ( t ) 2 ( t 8 ) ( t 6 ) ( t 1 ) 2 Now, P ' ( t ) 0 when t 8 and 6 and is undefined at t 1 But t 8 and 1 make no sense in terms of the physical situation, so we disregard them The only critical value is t 6 Figure 8 shows the sign chart for P ' ( t ) and indicates that 6 produces a relative minimum 5 Repeat example 5 using the function P ( t ) ( t 6 ) 2 t 1

Question

Example 5 A chemical company claims that 6 days after its new insecticide is applied to a one   acre field infested with a population of a certain insect, the population will be minimal  The company bases its claim on its belief that the function P ( t )   2   1 3 ( t   5 ) 2   t 1 1 5 , 0 t 2 0 accurately predicts the population size P ( in ten thousands ) of the insect t days after application  Assuming the population model is accurate, should the company 's claim be accepted or rejected  Solution A figure is not appropriate here  The company is making a claim about a function 's maximum value  Mathematically, this is a statement about the derivative of the function  Since we are given the function, we will differentiate it   P  ' ( t )   2 ( t 8 ) ( t   6 ) ( t 1 ) 2 Now, P  ' ( t )   0 when t     8 and 6 and is undefined at t     1   But t     8 and   1 make no sense in terms of the physical situation, so we disregard them  The only critical value is t   6   Figure 8 shows the sign chart for P  ' ( t ) and indicates that 6 produces a relative minimum  5   Repeat example 5 using the function P ( t )   ( t   6 ) 2 t 1

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Example 5 A chemical company claims that 6 days after its new insecticide is applied to a one - acre field infested with a population

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1 Understanding Responsive Design Principles

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