Saving Money
Your very generous grandparents give each grandchild \( \$ 10,000\) on their \(16th\) birthday to buy a new car. Since many of your friends have cars, and since you don’t have a job to earn gas money, you decide to wait to buy your first car. You find a bank that offers a CD with a rate of \(5\%\) APY. You decide to wait until you have \( \$15,000\) to buy your car. How long will it take for you to have \( \$ 15,000\)?
How did you solve this problem? Can you solve it another way?
Challenge: You have your eyes set on buying a Toyota Prius. A new Prius costs \(\$23,227\) and depreciates at a rate of \(11\%\) per year. Based on your savings rate above, and the depreciation of the Prius, when will you be able to afford a used Prius?
Hint: Think about the two functions. What would their graphs look like? How could the graphs help you figure out when you will have enough money to buy the car? Is there a way to solve this problem algebraically...with logs?
Solution solved multiple ways
Your very generous grandparents give each grandchild \( \$ 10,000\) on their \(16th\) birthday to buy a new car. Since many of your friends have cars, and since you don’t have a job to earn gas money, you decide to wait to buy your first car. You find a bank that offers a CD with a rate of \(5\%\) APY. You decide to wait until you have \( \$15,000\) to buy your car. How long will it take for you to have \( \$ 15,000\)?
How did you solve this problem? Can you solve it another way?
Challenge: You have your eyes set on buying a Toyota Prius. A new Prius costs \(\$23,227\) and depreciates at a rate of \(11\%\) per year. Based on your savings rate above, and the depreciation of the Prius, when will you be able to afford a used Prius?
Hint: Think about the two functions. What would their graphs look like? How could the graphs help you figure out when you will have enough money to buy the car? Is there a way to solve this problem algebraically...with logs?
Solution solved multiple ways