(a) Answer P = A ( 1 + r n ) − n t _ Explanation Given information : A = P ( 1 + r n ) n t 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 : 1 a m = a − m Calculation: Description Steps Use the symmetric property of inequality to rewrite the equation P ( 1 + r n ) n t = A Divide ( 1 + r n ) n t on both sides P ( 1 + r n ) n t / ( 1 + r n ) n t = A / ( 1 + r n ) n t Simplify fraction on both sides P = A / ( 1 + r n ) n t Use the exponent rule to rewrite right side of the equation P = A ( 1 + r n ) − n t (b) To determine To solve : the given equation for t Answer t = ( ln ( A / P ) ) / ( n ln ( 1 + r / n ) ) _ Explanation Given information : A = P ( 1 + r n ) n t 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 : ln m n = n ( ln m ) Calculation: Description Steps Use the symmetric property of inequality to rewrite the equation P ( 1 + r / n ) n t = A Divide P on both sides P ( 1 + r / n ) n t / P = A / P Simplify fraction on both sides ( 1 + r / n ) n t = A / P Take natural logarithm on both sides ln ( 1 + r / n ) n t = ln ( A / P ) Applying the rule ln m n = n ( ln m ) n t ⋅ ln ( 1 + r / n ) = ln ( A / P ) Dividing n ln ( 1 + r / n ) on both sides n t ⋅ ln ( 1 + r / n ) n ln ( 1 + r / n ) = ln ( A / P ) n ln ( 1 + r / n ) Simplifying fraction on both sides t = ( ln ( A / P ) ) / ( n ln ( 1 + r / n ) )

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.5, Problem 6E

(a)

To determine

To solve : the given equation for P

(a)

Expert Solution

Answer to Problem 6E

P=A(1+rn)−nt_

Explanation of Solution

Given information: A=P(1+rn)n t

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: 1am=a−m

Calculation:

Description	Steps
Use the symmetric property of inequality to rewrite the equation	P(1+rn)n t=A
Divide (1+rn)n t on both sides	P(1+ r n)n t/(1+ r n)n t=A/(1+ r n)n t
Simplify fraction on both sides	P=A/(1+ r n)n t
Use the exponent rule to rewrite right side of the equation	P=A(1+rn)− n t

(b)

To determine

To solve : the given equation for t

(b)

Expert Solution

Answer to Problem 6E

t=(ln(A/P))/(nln(1+r/n))_

Explanation of Solution

Given information: A=P(1+rn)n t

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: lnmn=n(lnm)

Calculation:

Description	Steps
Use the symmetric property of inequality to rewrite the equation	P(1+r/n)n t=A
Divide P on both sides	P(1+r/n)n t/P=A/P
Simplify fraction on both sides	(1+r/n)n t=A/P
Take natural logarithm on both sides	ln(1+r/n)n t=ln(A/P)
Applying the rule lnmn=n(lnm)	nt⋅ln(1+r/n)=ln(A/P)
Dividing nln(1+r/n) on both sides	nt⋅ln(1+r/n)nln(1+r/n)=ln(A/P)nln(1+r/n)
Simplifying fraction on both sides	t=(ln(A/P))/(nln(1+r/n))

Chapter 3.5, Problem 5E

Chapter 3.5, Problem 7E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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