PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Differential Equations
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Chapter 3.5, Problem 20E
To determine

Tocomplete:

The given table for a savings account which is compounded continuously.

Expert Solution & Answer
Check Mark

Answer to Problem 20E

The completed table is:

  Initial InvestmentAnnual % RateTime to DoubleAmount After10 Years1761.723.5%19.80$2500

Explanation of Solution

Given:

Rate of interest in a continuously compounded account is 3.5% and the amount after 10 years is $2500.

Formula used:

Amount in a continuously compounded account is given by:

  A=Pert

Calculation:

Upon substituting the given values in the formula for continuous compound interest, we get:

  2500=Pe(0.035×10)⇒2500=Pe(0.35)⇒P=2500e0.35⇒P=1761.72

We can rewrite the formula as: A=1761.72e0.035t

In order to find the doubling time, we will replace A by 3523.44 and solve for t as shown below:

  3523.44=1761.72e0.035t⇒e0.035t=2⇒0.035t=ln2⇒t=ln20.035≈19.80

Therefore, the complete table is:

  Initial InvestmentAnnual % RateTime to DoubleAmount After10 Years1761.723.5%19.80$2500

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Chapter 3.5, Problem 19E
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Chapter 3.5, Problem 21E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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SEE MORE TEXTBOOKS
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY