Explanation The values of a = 0.005 , m = $ 100 , B 0 = $ 100 . So, the initial condition is s ( 0 ) = 50 . Consider the given differential equation d B d t = a B + m . Simplify the differential equation as follows, d B d t = a B + m ∫ d B a B + m = ∫ d t ln | a B + m | = t + c Take exponential on both sides yields, a B + m = e t + c . Simplify further and substitute the given values as follows. B = e t + c − m a B = C e 0.005 t − 100 0.005 = C e 0.005 t − 20 , 000 Thus, the general solution of the given differential equation is B = C e 0.005 t − 20 , 000 , where C is an arbitrary constant

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 7, Problem 102RE

To determine

To solve: The initial value problem dBdt=aB+m for t≥0, with B(0)=B0 and find out when the balance will reach at $7500.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7, Problem 101RE

Chapter 8.1, Problem 1E

Students have asked these similar questions

Q. At time k=0, an initial investment of $1200 is made into a savings account that pays % interest compounded monthly. (The monthly interest rate is 0.0025.) Each month, after the initial investment, an additional $200 is added to the account. Let Y be the amount in the atcount at the end of k months. a. Write the difference equation satisfied by Yk Yk+1= b. The amount of money that will be in the account after 3 years is $ The amount of money that will be in the account after 4 years is $ The amount of money that will be in the account after 6 years is $ The amount of interest in the 6-year total is $ Yo=

Activity no. 11 1. Grace invested P 50,000 at 5%. How much should he invest at 8% to have a total earnings of P 4,900?

A universal life policy is issued to a life aged 45. Death benefit is 10,000 and the policyholder pays an annual premium of 200 at the beginning of each year. Expense charges are 30% of first year premium and 5% of renewal premiums. Interest credited is 6% per year and interest assumed in the cost of insurance is 4% per year. Cost of insurance is based on Makeham's mortality, H = 0.01+0.0001(1.05*). The account value at the beginning of the 7th year, before any premium is paid, is 1,500. Calculate, to the nearest integer, the account value at the end of the 7th year.

Chapter 7 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 7.1 - What change of variables would you use for the...Ch. 7.1 - Prob. 2E Ch. 7.1 - What trigonometric identity is useful in...Ch. 7.1 - Describe a first step in integrating x32x+4x1dx.Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Substitution Review Evaluate the following...Ch. 7.1 - Substitution Review Evaluate the following...Ch. 7.1 - Substitution Review Evaluate the following...Ch. 7.1 - Substitution Review Evaluate the following...

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.

The initial value problem d B d t = a B + m for t ≥ 0 , with B ( 0 ) = B 0 and find out when the balance will reach at $7500.

Solution Summary: The author explains how to solve the initial value problem dBt=aB+m and the general solution of the given differential equation.

Concept explainers

Videos

To solve: The initial value problem dBdt=aB+m for t≥0, with B(0)=B0 and find out when the balance will reach at $7500.

Want to see the full answer?

Chapter 7 Solutions