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City planners model the size of their city using the

function A’(t)=(-1/50)*t^2+2t+20, where A is...
City planners model the size of their city using the function A’(t)=(-1/50)*t^2+2t+20, where A is measured in square miles and t is the number of years after 2010. How fast will the city be growing when it reaches a size of 38mi^2? Suppose the population density of the city remains constant from year to year at 1000 people/mi^2. Determine the growth rate of the population in 2030.
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Answered in 2 hours by:
3/1/2018
Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,184
Experience: B.S. in Civil Engineering
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Hi,

Thank you for using the site, and thank you for requesting me. I'll be happy to help you with this.

Can you please clarify the equation given in the problem statement? The text indicates that "A" is the area of the city, in square miles, but the equation given is "A'(t)", which would seem to be the derivative of the size function. It would seem that either the function should be "A(t)", or that it really is "A'(t)" but there is some other information missing (such as the initial size of the city).

Thanks,

Ryan

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Customer reply replied 4 months ago
It should be A (t)
Customer reply replied 4 months ago
Why for pisewise function constrains on the variable change to strict? For example
x^2+1, if x <=0
2x^2+x+1, if x>0For derivative both inequalities will be strict.

Hi,

Thank you for the clarification. Here are the solutions:

Derivatives

As always, please feel free to ask if you have any additional questions about this.

Thanks,

Ryan

Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,184
Experience: B.S. in Civil Engineering
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