Let f(t) be the balance in a savings account at the end of t years and suppose y = f(t) satisfies the differential equation y' = 0.05y - 12,500.(a)Suppose that after one year the balance is $230,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time?(b)Write the differential equation in the form y' = k(y - M).(c)Describe the differential equation in words.%3D%3D(a) The balance is decreasing at a rate of $- 1000 per year.(b) y' = .05(y - 230000)(c) Choose the correct answer below.A. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always increasing.B. The rate of change of the savings account balance is proportional to the difference between the balance at the end of t years and $250,000.C. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always decreasing.D. The differential equation gives the account balance at any time, t.

Consider the given differential equation y' = 0.05y - 10,000 y' = 0.05(y - 200,000)

Let f(t) be the balance in a savings account at the end of t years and suppose y = f(t) satisfies the differential equation y' = 0.05y - 12,500. (a)Suppose that after one year the balance is $230,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y'= k(y - M). (c)Describe the differential equation in words. (a) The balance is decreasing at a rate of $- 1000 per year. (b) y' = 05(y - 230000) (c) Choose the correct answer below. O A. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always increasing. B. The rate of change of the savings account balance is proportional to the difference between the balance at the end of t years and $250,000. C. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always decreasing. D. The differential equation gives the account halance at any time

Let f(t) be the balance in a savings account at the end of t years and suppose y = f(t) satisfies the differential equation y' = 0.05y - 12,500. (a)Suppose that after one year the balance is $230,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y'= k(y - M). (c)Describe the differential equation in words. (a) The balance is decreasing at a rate of $- 1000 per year. (b) y' = 05(y - 230000) (c) Choose the correct answer below. O A. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always increasing. B. The rate of change of the savings account balance is proportional to the difference between the balance at the end of t years and $250,000. C. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always decreasing. D. The differential equation gives the account halance at any time

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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Let f(t) be the balance in a savings account at the end of t years and suppose y = f(t) satisfies the differential equation y' = 0.05y - 12,500.
(a)Suppose that after one year the balance is $230,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time?
(b)Write the differential equation in the form y' = k(y - M).
(c)Describe the differential equation in words.
%3D
%3D
(a) The balance is decreasing at a rate of $
- 1000 per year.
(b) y' = .05(y - 230000)
(c) Choose the correct answer below.
A. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always increasing.
B. The rate of change of the savings account balance is proportional to the difference between the balance at the end of t years and $250,000.
C. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always decreasing.
D. The differential equation gives the account balance at any time, t.

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