Balanced Smith
Posted December 23, 2008
By admin
Balanced Smith
Differential equation word problem?
Mrs. Smith won 10,000,000 dollars in the lottery in 1997 and put the money in a bank account earning 8% interest per year, compounded continuously. Since then, Mrs.Smith has been spending money in this account continuously at a constant rate of S dollars per year.
Write the differential equation and initial condition that describes the balance B(t) in Mrs Smith's bank account?
Solve.
dB/dt = .08B - tS and B(0)=10^7
B ' - .08B = -tS
e^(-.08t) B ' - e^(-.08t) .08 B = - e^(-.08t) t S
[e^(-.08t) B ] ' = - e^(-.08t) t S
e^(-.08t) B = integral - e^(-.08t) t S
- e^(-.08t) B = -Se^(-.08t)( (t/.08) + (1/.08^2) )+ C)
B = S ((t/.08) + (1/.08^2) - Ce^(.08t))
The condition B(0)=10^7 implies C = 1/(.08)^2 - (10^7 / S)
B = S ( t/.08 + 1/(.08)^2 - (e^(.08t)/(.08^2)) + (1(0^7e^(.08t))/S))
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Yukon Counter Balanced Smith Machine This machine is perfect for those who are serious about weight training. Yukon's Counter Balanced Smith Machine provides amazing versatility for a smooth self-spotting workout! The Unique Linear Bearing system is constantly circulating to provide three times the load capacity and twenty-seven times the travel life of ordinary bearings giving you the same benefits of a free weight workout with the safety of the best weight stack machine. This makes for the ultimate primary and secondary muscle group development and leads to a faster more productive route to achieving your fitness goals. Plate Type: Olympic Weights sold separately. Product Features: Self Spotting Weight bar counter balanced at 15lbs. Counter weight shielded with smoked Plexiglas Has 6 Olympic weight pegs covered with PVC for easy on/off action and convenient plate storage 1000lbs. Test knurled Olympic weight bar Fully adjustable bronzed bushed safety spotters 14 different height lock outs Dimensions: 84"H x 84"W x 66"D Limited Lifetime Warranty. |
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