Percent Change

This activity is designed to reinforce objectives 2.6, 5.1, 5.2, 5.3, and 6.3.

Many things don't change at a constant rate, though they do change by a constant percent. For example, loans and credit card debts accrue interest at a certain percent rate. In the same way, savings accounts earn interest at a fixed percent rate.

A percent change is not always an increase. For example, caffeine is removed from an average person's bloodstream at a rate of about 11.5% per hour (Statland & Demas, 1980). That means if Joe drinks 200 mg of caffeine in his coffee at 8:00 a.m., then he will have about 177 mg left in his bloodstream at 9:00 a.m. and about 123 mg by noon, four hours later.

Here is how you can find those values.

For the first estimate, take 11.5% of the starting amount, the initial 200 mg, and subtract:

200 mg x 0.115 = 23 mg
200 mg - 23 mg = 177 mg

To find the second estimate, you want to know the amount remaining after three more hours, so repeat those same steps three more times. Find 11.5% and subtract it:

177 mg × 0.115 = 20.335 mg
177 mg - 20.355 mg = 156.645 mg

156.645 × 0.115 = 18.014...
156.645 mg - 18.014... mg = 138.630... mg

138.630... mg × 0.115 = 15.942... mg
138.630... mg - 15.942... mg = 122.688... mg
This rounds to 123 mg.

There's a much easier way to find those estimates. Notice that since you are subtracting 11.5% of the amount, you are keeping 88.5% of the amount. You can just find 88.5% four times; in other words, we can just multiply by 0.885 four times:

200 mg × 0.885 × 0.885 × 0.885 × 0.885 = 200 mg x (0.885)4 = 122.688... mg

Again, this rounds to 123 mg.

Instructions

For this assignment, think of an example of something that you can research to find a percent change. You might look up drug information like the example above. You might search for a loan or a credit card offer.

Address the following in a Microsoft Word document:

• Briefly describe your example and why a percent change is appropriate.
• Identify the website or other resource you used to find information.
• Find the percent change for the example you researched. Is it an increase or a decrease? How frequently does your amount increase or decrease by that percent? Every hour? Every year?
• Provide a starting point based on your situation. In the example above, the initial 200 mg is the starting point. Maybe in your example, you would give a starting balance on a credit card.
• Use your starting point and percent change to find two estimates for future values. In the example above, the two estimates were 177 mg at 9:00 a.m. an

 

 

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