Calculus Proect 1 Part 2 Choudhary

Calculus Proect 1 Part 2 Choudhary - Choudhary 1 Abusufian...

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Choudhary 1 Abusufian Choudhary Mr. Long Calculus 1 8 November 2015 Project Part 2 Function: f ( x ) = 1000 1 + 50 e 0.4 t Domain of the function: ¿ . The domain of the function is restricted to the positive real numbers only because time cannot be in negative. Range of the function: ( 19.6078,1000 ) . In context of the problem this means that the rumor will spread up to a 1000 people. And it starts from 19 people because the rumor has to start spreading from somewhere. Intercepts: y-intercept, y=19.6078. This means that on day 0 about 19 people knew the rumor and from there it started spreading to other people. There are no x-intercepts for this function because the rumor is always spreading. Continuity, Differentiability & Special points (Maximum, Minimum): Derivative: f ' ( x ) = 20000 e 0.4 t ( 50 + e 0.4 t ) 2 the derivative of the function is positive on the domain ( 0, ) which means that the function is always increasing and differentiable on the domain and in context of the problem it means that the rumor was always spreading to more and more people until it reaches up to a 1000 people. Since the function is always increasing on the domain
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Choudhary 2 and there is no end point of the domain, the function does not have a maximum. However, it does have a minimum since the starting point of the domain is inclusive. The minimum is global and
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