Tiered Problems for a Variety of Middle School ... - WordPress.com

Grade 8 Goal: Apply Exponential (Growth) Functions
Green
You deposit $500 into an account that pays 8% interest compounded yearly. Write a
function to represent your account’s balance B after x years. What will the account balance
be after 6 years?
Blue
Copying Conundrum: We have a copy machine in the office that will let you increase or
decrease the size of a picture by a certain percentage. For example, if I have a picture that is
4 inches by 6 inches and I copy it at 50%, the dimensions on the copy will be 2 inches by 3
inches.
Start with an 8-inch by 10-inch picture. Copy it at 80%, then copy the copy at 80%, and
continue this process until you have 5 copies of the original, each of which is smaller than
the previous one. Write a formula that will allow you to easily find the picture's largest
dimension after doing this n times.
Black
There are 100 rats in a given population. At first, and under ideal circumstances, the rat
population increases 20% per month. After 2 months, some bait is laid that contains a
substance that slows their population growth. For one month the population remains
constant. After that, the population starts to decrease by 50% per month.
There are three parts to this story. Find the function that matches each part of the story (if
your function contains decimal values, round those values to the nearest whole number).
Also, create a single graph that illustrates all three parts of this story.
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