Modeling a Context from a Verbal Description
Christine has $500 to deposit in a savings account, and she is trying to decide between two banks. Bank A offers 10% annual interest compounded quarterly. Rather than compounding interest for smaller accounts, Bank B offers to add $15 quarterly to any account with a balance of less than $1,000 for every quarter, as long as there are no withdrawals. Christine has decided that she will neither withdraw, nor make a deposit for a number of years.
Develop a model that will help Christine decide which bank to use.
Alex designed a new snowboard. He wants to market it and make a profit. The total initial cost for manufacturing setup, advertising, etc. is $500,000, and the materials to make the snowboards cost $100 per board.
The demand function for selling a similar snowboard is 𝐷(𝑝) = 50,000 − 100𝑝, where 𝑝 represents the selling price (in
dollars) of each snowboard.
a. Write an expression for each of the following in terms of 𝑝.
Demand Function (number of units that will sell)
Revenue [(number of units that will sell)(price per unit, 𝑝)]
Total Cost (cost for producing the snowboards)
b. Write an expression to represent the profit.
c. What is the selling price of the snowboard that will give the maximum profit?
d. What is the maximum profit Alex can make?
Alvin just turned 16 years old. His grandmother told him that she will give him $10,000 to buy any car he wants whenever he is ready. Alvin wants to be able to buy his dream car by his 21st birthday, and he wants a 2009 Avatar Z, which he could purchase today for $25,000. The car depreciates (reduces in value) at a rate is 15% per year. He wants to figure out how long it would take for his $10,000 to be enough to buy the car, without investing the $10,000.
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