Suppose that $50,000 from a retirement account is invested in a large cap stock fund. After 20 yr. the value is $194 .,809 .67 . a. Use the model A = P e r t to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. b. How long will it take the investment to reach one-quarter million dollars? Round to the nearest tenth of a year.
Suppose that $50,000 from a retirement account is invested in a large cap stock fund. After 20 yr. the value is $194 .,809 .67 . a. Use the model A = P e r t to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. b. How long will it take the investment to reach one-quarter million dollars? Round to the nearest tenth of a year.
Solution Summary: The author calculates the average rate of return of an invested amount under continuous compounding by using the model equation A=Pert.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
1. Solve the initial value problem:
y" -11y' + 30y = x³e6x
y(0) 11, y'(0) = 36
=
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