Explanation Given information: An investment account grows at an annual rate of 10 % compounded continuously. The account was open with an initial deposit of $1500 and monthly deposits of $ 800 are made into the account. Formula used: The solution of initial value problem y ' = r y + k , y 0 = p 0 is y = p 0 + k r e r t − k r . Calculation: If no deposits or withdrawals are made, then only interest is being added to the account at a rate proportional to the amount in the account with constant of proportionality r = 10 % = 0.1 . In this case growth of P t comes from interest only and which satisfies the equation, y ' = 0.1 × y Taking the deposits into consideration which are added into the account at the rate of $ 800 per month i.e., $ 9600 per year then the amount of money in the account changes in two ways − the rate at which interest is added and the rate at which deposits are made. The rate of change of P t is the net effect of these two influences and it satisfies the differential equation- y ' = 0.1 y + 9600 Since the initial deposit in the account was $ 1500 , it follows that P t satisfies the initial condition y 0 = 1500

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 5.4, Problem 10E

To determine

To find: Pt in Exercise 4 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.4, Problem 9E

Chapter 5.4, Problem 11E

Students have asked these similar questions

Calculus lll May I please have the solutions for the following examples? Thank you

Calculus lll May I please have the solutions for the following exercises that are blank? Thank you

The graph of 2(x² + y²)² = 25 (x²-y²), shown in the figure, is a lemniscate of Bernoulli. Find the equation of the tangent line at the point (3,1). -10 Write the expression for the slope in terms of x and y. slope = 4x³ + 4xy2-25x 2 3 4x²y + 4y³ + 25y Write the equation for the line tangent to the point (3,1). LV Q +

Chapter 5 Solutions

Calculus & Its Applications

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

P t in Exercise 4 .

Solution Summary: The author explains that an investment account grows at an annual rate of 10% compounded continuously.

Concept explainers

Videos

To find: Pt in Exercise 4 .

Want to see the full answer?

Chapter 5 Solutions