# rate of change problem

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• March 17th 2013, 01:40 AM
asifrahman1988
rate of change problem
Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is

dx
dt = 5000(1−(100/(t+10)^2)) calculators per week.

(Notice that production approaches 5000 per week as time goes on, but the initial production is lower because ot the workers’ unfamiliarity with the new techniques.) Find the number of calculators produced from the beginning of the third week to the end of the fourth week
• March 17th 2013, 02:40 AM
Prove It
Re: rate of change problem
Your equation is $\displaystyle \frac{dx}{dt} = 5000 \left( 1 - \frac{100}{(t + 10)^2} \right)$.

Rewrite this as $\displaystyle \frac{dx}{dt} = 5000 - 500\,000(t + 10)^{-2}$ and integrate.