EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Differential Equations
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Chapter 3.5, Problem 8E
To determine

To find : the time to double and amount after 10 years.

Expert Solution & Answer
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Answer to Problem 8E

The time to double is   t≈6.6 years    _

The amount after 10 years is   A≈$2143.24    _

Explanation of Solution

Given information : Initial Investment is $750 & Annual percentage Rate is 1012%

Concept Involved:

Solving for a variable means getting the variable alone in one side of the equation by undoing whatever operation is done to it.

Formula Used:

For continuous compounding, after t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the formula: A = Pert

Logarithmic property: lneX=X

Calculation:

    DescriptionSteps
    Substitute the given information in the formula A = Pert {P=750, r = 0.105}A=750e0.105t
    To find the time to double, we need to replace 1500 in place of A1500=750e0.105t
    Use symmetric property of equality which states that if a = b then b = a to rewrite the equation750e0.105t=1500
    Divide by 750 on both sides750e0.105t750=1500750
    Simplify fraction on both sides of the equatione0.105t=2
    Take natural logarithm on both sideslne0.105t=ln(2)

Calculation (Continued):

    DescriptionSteps
    Apply the logarithmic rule lneX=X in left side of the equation 0.105t=ln2
    Divide by 0.105 on both sides 0.105t0.105=ln20.105
    Simplify fraction on both sides of the equationt=6.6 years
    To find the amount after 10 years substitute 10 for t in the equation A=750e0.105tA=750e0.105( 10)      =750e1.05      ≈$2143.24

Conclusion:

    Initial Investment Annual % Rate Time to Double Amount After 10 years
    $750 (Given)1012%(Given) 6.6 years $2143.24
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Chapter 3.5, Problem 7E
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Chapter 3.5, Problem 9E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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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