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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4, Problem 129RE
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Calculus: An Applied Approach (Min...

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Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Modeling Compound Interest In Exercises 127-130, complete the table for an account in which interest is compounded continuously.

Initialinvestment Annualrate Time to double Amount after 10 years Amount after 25 years
129. $15,000 $18,321.04

To determine

To calculate: The accumulated amount of an investment of $15,000 after 25 years if the amount after 10 years is $18,321.04 and also calculate the time for the investment to double and the annual rate of interest.

Explanation

Given Information:

The provided information is that the amount after 10 years is $18,321.04 and the initial investment is $15,000.

Formula used:

The accumulated amount for an initial investment P compounded continuously at an annual rate of interest r is given by the exponential growth model, A=Pert.

Calculation:

Consider the provided information that the amount after 10 years is $18,321.04 and the initial investment is $15,000.

Here, P=$15,000 and at time t=10, A=18,321.04.

Substitute t=10, P=$15,000 and A=18,321.04 in the exponential growth model A=Pert,

18321.04=15000er×10e10r=18321.0415000

Take natural log on both the sides,

ln(e10r)=ln (18321.0415000)10r⋅lne=ln (18321.0415000)r=ln (18321.0415000)10r≈0.02

Hence, the annual rate or interest is 2%.

Substitute P=15000 and r=0.02 in the exponential growth model A=Pert,

A=15000e0

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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P-4CPSect-4.6 P-1SWUSect-4.6 P-2SWUSect-4.6 P-3SWUSect-4.6 P-4SWUSect-4.6 P-5SWUSect-4.6 P-6SWUSect-4.6 P-7SWUSect-4.6 P-8SWUSect-4.6 P-9SWUSect-4.6 P-10SWUSect-4.6 P-11SWUSect-4.6 P-12SWUSect-4.6 P-1ESect-4.6 P-2ESect-4.6 P-3ESect-4.6 P-4ESect-4.6 P-5ESect-4.6 P-6ESect-4.6 P-7ESect-4.6 P-8ESect-4.6 P-9ESect-4.6 P-10ESect-4.6 P-11ESect-4.6 P-12ESect-4.6 P-13ESect-4.6 P-14ESect-4.6 P-15ESect-4.6 P-16ESect-4.6 P-17ESect-4.6 P-18ESect-4.6 P-19ESect-4.6 P-20ESect-4.6 P-21ESect-4.6 P-22ESect-4.6 P-23ESect-4.6 P-24ESect-4.6 P-25ESect-4.6 P-26ESect-4.6 P-27ESect-4.6 P-28ESect-4.6 P-29ESect-4.6 P-30ESect-4.6 P-31ESect-4.6 P-32ESect-4.6 P-33ESect-4.6 P-34ESect-4.6 P-35ESect-4.6 P-36ESect-4.6 P-37ESect-4.6 P-38ESect-4.6 P-39ESect-4.6 P-40ESect-4.6 P-41ESect-4.6 P-42ESect-4.6 P-43ESect-4.6 P-44ESect-4.6 P-45ESect-4.6 P-46ECh-4 P-1RECh-4 P-2RECh-4 P-3RECh-4 P-4RECh-4 P-5RECh-4 P-6RECh-4 P-7RECh-4 P-8RECh-4 P-9RECh-4 P-10RECh-4 P-11RECh-4 P-12RECh-4 P-13RECh-4 P-14RECh-4 P-15RECh-4 P-16RECh-4 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Contemporary Mathematics for Business & Consumers

For Exercises 14 and 15, let m1=x and m2=y. Using variables x and y, write an equation that expresses the fact ...

Elementary Geometry For College Students, 7e

Finding an Indefinite Integral In Exercises 53-62, find the indefinite integral. e1/xx2dx

Calculus: Early Transcendental Functions (MindTap Course List)

Approximating Inverse Trigonometric Functions In Exercises 15-18, use a calculator to approximate the value. Ro...

Calculus of a Single Variable

In Exercise 14, determine which of the following are regular stochastic matrices. [12013001312113].

Finite Mathematics for the Managerial, Life, and Social Sciences

The salaries of a secretary, a salesperson, and a vice president for a retail sales company are in the ratio 2:...

Elementary Geometry for College Students

Finding a Limit In Exercises 25-36, find the limit (if it exists). If the limit does not exist, explain why. li...

Multivariable Calculus

Proof Prove that for any real number y there exists x in (2,2) such that tan x=y.

Calculus

Which number is the best choice for the value of a in the following graph? a) e b) 1 c) 2 d) 3

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding a Limit In Exercises 39-50, find the limit (if it exists). If it does not exist, explain why. limx4x1

Calculus (MindTap Course List)

For and , a × b =

Study Guide for Stewart's Multivariable Calculus, 8th

Refer to the data in exercise 2. The estimated regression equation for those data is = 18.4 + 2.01x1 + 4.74x2 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Practice Use the graph of the function f shown to determine each of the following. f-11

College Algebra (MindTap Course List)

Identify the characteristics that differentiate different sets of data and identify the hypothesis test(s) appr...

Research Methods for the Behavioral Sciences (MindTap Course List)

The following data give the percentage of women working in five companies in the retail and trade industry. The...

Statistics for Business & Economics, Revised (MindTap Course List)

Define cross-sectional and longitudinal designs, identify these designs when they appear in a research report, ...

Research Methods for the Behavioral Sciences (MindTap Course List)

In each of the following problems, refer to the corresponding figure. Write an equation, solve for x, and check...

Mathematics For Machine Technology

The article Reduction is Soluble Protein and Chlorophyll Contents in a Few Plants as Indicators of Automobile E...

Introduction To Statistics And Data Analysis

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