Explanation Given information: Consider the balance B ( t ) of a bank account with initial balance B ( 0 ) = B 0 . We are withdrawing money at a continuous rate r (in euro/year). The interest rate is k (%/year), compounded continuously. Calculation: The required differential equation is d B ( t ) d t = R % of B ( t ) − r % of B ( t ) d B ( t ) d t = ( R 100 − r 100 ) B ( t ) d B ( t ) d t = R − r 100 B ( t ) By separating variables we get d B B = R − r 100 d t Now we integrate to get In B = R − r 100

5th Edition

ISBN: 9780321796943

Author: BRETSCHER, Otto.

Publisher: Pearson Education

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 9.3, Problem 32E

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To set up: a differential equation for B(t) and solve it in terms of B0,r and k . Sketch a graph for B(t) in each case.

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Chapter 9.3, Problem 31E

Chapter 9.3, Problem 33E

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Linear Algebra With Applications

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To set up: a differential equation for B ( t ) and solve it in terms of B 0 , r and k . Sketch a graph for B ( t ) in each case.

Solution Summary: The author sets up a differential equation for B(t) and solves it in terms of B_0,r and k.

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To set up: a differential equation for B(t) and solve it in terms of B0,r and k . Sketch a graph for B(t) in each case.

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Chapter 9 Solutions