A university wants to establish a fund to support meal plans for students. The fund will be used to distribute $10k in yearly fellowships, and will operate by an investment-fund model: after an initial donation, the only income will be the interest on the amount of money in the fund. The school decided to model the amount of money in the fund at a given time t, A(t), by a differential equation dA = 0.02A – s, dt where s = $10k/year is the scholarship amount they want to distribute per year and 0.02 is the estimated interest rate. 1. Find all solutions to the differential equation.
A university wants to establish a fund to support meal plans for students. The fund will be used to distribute $10k in yearly fellowships, and will operate by an investment-fund model: after an initial donation, the only income will be the interest on the amount of money in the fund. The school decided to model the amount of money in the fund at a given time t, A(t), by a differential equation dA = 0.02A – s, dt where s = $10k/year is the scholarship amount they want to distribute per year and 0.02 is the estimated interest rate. 1. Find all solutions to the differential equation.
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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Transcribed Image Text:A university wants to establish a fund to support meal plans for students. The fund will be used
to distribute $10k in yearly fellowships, and will operate by an investment-fund model: after an initial
donation, the only income will be the interest on the amount of money in the fund. The school decided to
model the amount of money in the fund at a given time t, A(t), by a differential equation
dA
0.02A
dt
where s =
$10k/year is the scholarship amount they want to distribute per year and 0.02 is the estimated
interest rate.
1. Find all solutions to the differential equation.
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