A student decides to save money for a trip to Uluru. She opens a savings account with $300, and sets up a daily automatic transfer of 2 from her regular account into her savings account. The bank pays 5.5% interest per year into her savings account, compounded continuously. The student plans to withdraw the money from the bank at the end of two years. She is, however, worried that she isn't saving enough, and decides to model the problem to find out how much she will have at the end of two years. Let M(t) be the amount of money in her savings account at time t. She opens the account at time t = 0. Assume that one year has 365 days. (a) Her first model is the following, with time in years: dM 0.06M+2, dt = M(0) = 300.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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7. A student decides to save money for a trip to Uluru. She opens a savings account with
$300, and sets up a daily automatic transfer of 2 from her regular account into her savings
account. The bank pays 5.5% interest per year into her savings account, compounded
continuously. The student plans to withdraw the money from the bank at the end of two
years. She is, however, worried that she isn't saving enough, and decides to model the
problem to find out how much she will have at the end of two years. Let M(t) be the
amount of money in her savings account at time t. She opens the account at time t 0.
Assume that one year has 365 days.
(a) Her first model is the following, with time in years:
dM
dt
= 0.06M + 2, M(0) = 300.
A friend of hers tells her that there is a problem with this model. What is the prob-
lem?
(b) She realizes where she went wrong, and fixes her model. There are two standard
ways to fix it, using time in years or using time in days. Make a choice, and fix the
model.
(c) Solve the corrected model and answer: How much money was in the savings account
after two years?
Transcribed Image Text:7. A student decides to save money for a trip to Uluru. She opens a savings account with $300, and sets up a daily automatic transfer of 2 from her regular account into her savings account. The bank pays 5.5% interest per year into her savings account, compounded continuously. The student plans to withdraw the money from the bank at the end of two years. She is, however, worried that she isn't saving enough, and decides to model the problem to find out how much she will have at the end of two years. Let M(t) be the amount of money in her savings account at time t. She opens the account at time t 0. Assume that one year has 365 days. (a) Her first model is the following, with time in years: dM dt = 0.06M + 2, M(0) = 300. A friend of hers tells her that there is a problem with this model. What is the prob- lem? (b) She realizes where she went wrong, and fixes her model. There are two standard ways to fix it, using time in years or using time in days. Make a choice, and fix the model. (c) Solve the corrected model and answer: How much money was in the savings account after two years?
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