menu
Hit Return to see all results
Chapter 12.5, Problem 41E
BuyFindarrow_forward

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Investing When the interest on an investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the account. That is, if the amount present is P, then d P d t = k P where P is in dollars, t is in years, and k is a constant. If $100,000 is invested (when t = 0) and the amount in the account after 15 years is$211,700, find the function that gives the value of the investment as a function of t. What is the interest rate on this investment?

To determine

To calculate: The investment function after time t, and also interest rate of the investment if the amount in the amount in the account is dPdt=kP. Where P is in dollars, t is in the years, and k is a constant. If $100,000 is invested and the amount in the account after 15 years is$211,700.

Explanation

Given Information:

The investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the amount in the account.

dPdt=kP

Where P is in dollars, t is in the years, and k is a constant.

If $100,000 is invested and the amount in the account after 15 years is$211,700.

Formula used:

Separable equation is of the form:

g(y)dy=f(x)dx

Integration on both the sides yields the solution of this equation.

Calculation:

Consider the investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the amount in the account.

dPdt=kP

Where P is in dollars, t is in the years, and k is a constant.

If $100,000 is invested and the amount in the account after 15 years is$211,700.

Firstly, separate the above differential equation as:

dPP=kdt

Integrate the provided function as:

dPP=kdtlnP=kt+CP=ekt+CP=Cekt

At the given condition t=0,P=100,000 put in the above equation as:

P=Cekt100,<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

## Additional Math Solutions

#### Find more solutions based on key concepts

Show solutions add

#### Compute P5,2.

Understanding Basic Statistics

#### In Exercises 49-62, find the indicated limit, if it exists. 62. limx24x22x2+x3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the expression sin Exercises 116. (14)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### List all of the subsets of {a, b, c, d}.

Mathematical Excursions (MindTap Course List)

#### Multiply: (9)(1)

Elementary Technical Mathematics

#### In Exercises 116, determine whether the argument is valid. pq~p~q

Finite Mathematics for the Managerial, Life, and Social Sciences

#### Find each value of x. log7x=0

College Algebra (MindTap Course List)