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 16E
To determine

Tocomplete:

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

Expert Solution & Answer
Check Mark

Answer to Problem 16E

The completed table is:

  Initial InvestmentAnnual % RateTime to DoubleAmount After10 Years$10005.78%12$1782.47

Explanation of Solution

Given:

Initial investment in a continuously compounded account is $1000 and it doubles in 12 years.

Formula used:

Amount in a continuously compounded account is given by:

  A=Pert

Calculation:

We have been given the initial investment as $1000 and time to double is 12 years.Upon substituting these values in the formula for continuously compounded interest, we get:

  2000=1000er(12)⇒e12r=20001000=2⇒12r=ln2⇒r=ln212≈0.05776=5.78%

We can rewrite the formula as: A=1000e0.0578t

In order to find the amount after 10 years, we will substitute t=10 and solve for A as shown below:

  A=1000e0.0578(10)⇒A=1000e0.578⇒A=1000(1.7824699)⇒A=1782.47

Therefore, the complete table is:

  Initial InvestmentAnnual % RateTime to DoubleAmount After10 Years$10005.78%12$1782.47

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Chapter 3.5, Problem 15E
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Chapter 3.5, Problem 17E

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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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