2) The rate of increase in a bank account is 4% of the amount in the account; the initial depositis $1000.a) State the rate of change of the amount in the bank account as a differential equation.b) Solve this diffy q to find an equation that describes the amount of money in the accountas a function of time, with t = 0 as the time of the initial deposit of $1000.c) Explain and show why 4% is called the constant of proportionality, and how theequations found in question a) and question b) relate.d) Explain and show how to derive continuous compound interest formula. Explain how itrelates to this problem (this should be obvious!). The compound interest formula iseasily found and is commonly found in algebra 2 and precalculus textbooks, such as thisimage I got from a precalculus text from my classroom:If P dollars is invested at an annual interest rate of r,compounded continuously, then A is the amount aftert years.A = Pet

Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is $1000. a) State the rate of change of the amount in the bank account as a differential equation. b) Solve this diffy q to find an equation that describes the amount of money in the account as a function of time, with t = 0 as the time of the initial deposit of $1000. c) Explain and show why 4% is called the constant of proportionality, and how the equations found in question a) and question b) relate.

The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is $1000. a) State the rate of change of the amount in the bank account as a differential equation. b) Solve this diffy q to find an equation that describes the amount of money in the account as a function of time, with t = 0 as the time of the initial deposit of $1000. c) Explain and show why 4% is called the constant of proportionality, and how the equations found in question a) and question b) relate.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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 differential equations.

Question

2) The rate of increase in a bank account is 4% of the amount in the account; the initial deposit
is $1000.
a) State the rate of change of the amount in the bank account as a differential equation.
b) Solve this diffy q to find an equation that describes the amount of money in the account
as a function of time, with t = 0 as the time of the initial deposit of $1000.
c) Explain and show why 4% is called the constant of proportionality, and how the
equations found in question a) and question b) relate.
d) Explain and show how to derive continuous compound interest formula. Explain how it
relates to this problem (this should be obvious!). The compound interest formula is
easily found and is commonly found in algebra 2 and precalculus textbooks, such as this
image I got from a precalculus text from my classroom:
If P dollars is invested at an annual interest rate of r,
compounded continuously, then A is the amount after
t years.
A = Pet

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