Congratulations, you just won the lottery! In one option presented to you, you will be paid one million dollars a year for the next 25 years. You can deposit this money in an account that will earn 5% each year. (a) Let M(t) be the amount of money in the account (measured in millions of dollars) at time t (measured in years). Set up a differential equation that describes the rate of change in the amount of money in the account. Two factors cause the amount to grow – first, you are depositing one millon dollars per year and second, you are earning 5% interest. (b) If there is no amount of money in the account when you open it, how much money will you have in the account after 25 years? (c) The second option presented to you is to take a lump sum of 10 million dollars, which you will deposit into a similar account. Set up a new initial value problem (that is, differential equation with initial condition) to model this situation. (d) How much money will you have in the account after 25 years with in this case? (e) Do you prefer the first or second option? Explain your thinking. (f) At what time does the amount of money in the account under the first option overtake the amount of money in the account under the second option?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Congratulations, you just won the lottery! In one option presented to you, you will be paid one
million dollars a year for the next 25 years. You can deposit this money in an account that will earn
5% each year.
(a) Let M(t) be the amount of money in the account (measured in millions of dollars) at time
t (measured in years). Set up a differential equation that describes the rate of change in the
amount of money in the account. Two factors cause the amount to grow – first, you are
depositing one millon dollars per year and second, you are earning 5% interest.
(b) If there is no amount of money in the account when you open it, how much money will you
have in the account after 25 years?
(c) The second option presented to you is to take a lump sum of 10 million dollars, which you
will deposit into a similar account. Set up a new initial value problem (that is, differential
equation with initial condition) to model this situation.
(d) How much money will you have in the account after 25 years with in this case?
(e) Do you prefer the first or second option? Explain your thinking.
(f) At what time does the amount of money in the account under the first option overtake the
amount of money in the account under the second option?
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