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course MTH 173
5/12 1AM
Write the differential equation expressing the hypothesis that the rate of change of an investment is proportional to the principal P. Evaluate the proportionality constant if it is known that the when the principal is 2915 its rate of change is 300. If this is the t=0 value of the principal, then approximately what will be the principal at t = 1.2? What then will be the principal at t = 2.4? SOLUTION:
2915y = 300
y = .1029k
Constant is .1029
`dy/`dx = .1029
`dy = .1029 `dx
`dx = 1.2
`dy = .1029(1.2) = .1235
300 + .1235
At t = 1.2, principle will be 300.1235
`dx = (2.4 - 1.2) = 1.2
300.1235 + .1235
At t = 2.4, principle will be 300.247"
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You haven't written the differential equation expressing the stated proportionality between the rate of change of the investment and the principle.
How would you symbolize the rate of change of the principal with respect to time?
How would you then symbolize the proportionality?
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