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. 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

a) The initial amount in the bank account is P=$1000. The rate of increment of the amount is…

Answered: 2) The rate of increase in a bank…

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.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 37CT: On the day a grandchild is born, a grandparent deposits $2500 in a fund earning 7.5% interest,...

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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.

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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