IM Alg.1.5.4 Lesson: Understanding Decay
What do you notice? What do you wonder?
Here is one way to think about how much Diego has left after spending of $100. Explain each step. Step 1:
Step 2:
Step 3:
Step 4:
A person makes $1,800 per month, but of that amount goes to her rent. What two numbers can you multiply to find out how much she has after paying her rent?
Write an expression that only uses multiplication and that is equivalent to reduced by of .
Every year after a new car is purchased, it loses of its value. Let’s say that a new car costs $18,000. A buyer worries that the car will be worth nothing in three years. Do you agree? Explain your reasoning.
Write an expression to show how to find the value of the car for each year listed in the table.
Write an equation relating the value of the car in dollars, , to the number of years, .
Use your equation to find when is 0. What does this value of mean in this situation?
A different car loses value at a different rate. The value of this different car in dollars, , after years can be represented by the equation . Explain what the numbers 10,000 and mean in this situation.
Start with an equilateral triangle with area 1 square unit, divide it into 4 congruent pieces as in the figure, and remove the middle one.
Then, repeat this process with each of the remaining pieces. Repeat this process over and over for the remaining pieces. The figure shows the first two steps of this construction.
What fraction of the area is removed each time?
How much area is removed after the -th step? Use a calculator to find out how much area remains in the triangle after 50 such steps have been taken.