When an original amount is reduced by a consistent rate over a period of time, exponential decay is happening. The purpose of this page is to learn more about that consistent rate, the decay factor, and percent change. This page gives the answers and explanations to the worksheet, Exponential Decay and Percent Change.
Percent Decrease in Real Life: Politicians Balk at Salt
Recently, a lawmaker announced legislation that will force us in the land of the free and the brave to cut back on the salt that we crave. What if the salt reduction law passed, and we consumed less of the white stuff?
Suppose that each year, restaurants will be mandated to decrease sodium levels by 2.5% annually, beginning in 2011. The predicted decline in heart attacks can be described by the following function:
y = 10,000,000(1-.10)x , where y respresents the annual number of heart attacks after x years.
Apparently, the legislation will be worth its salt. Americans will be afflicted with fewer strokes.
Here are my fictional projections for annual strokes in America:
- 2010: 7,000,000 strokes
- 2011: 6,650,000 strokes
- 2012: 6,317,500 strokes
- 2013: 6,001,625 strokes
(Note: I make up these numbers for math sakes! Please contact your local salt expert or cardiologist for real data.)
Answers and Explanations
1. What is the mandated percent decrease for salt consumption in restaurants?
Answer: 2.5%
Explanation: Be careful, three different things - sodium levels, heart attacks, and strokes - are predicted to decrease. Each year, restaurants will be mandated to decrease sodium levels by 2.5% annually, beginning in 2011.
2. What is the mandated decay factor for salt consumption in restaurants?
Answer: .975
Explanation: Decay factor: (1 - b) = (1-.025) = .975
3. Based on predictions, what will be the percent decrease for annual heart attacks?
Answer: 10%
Explanation: The predicted decline in heart attacks can be described by the following function:
y = 10,000,000(1-.10)x , where y respresents the annual number of heart attacks after x years.
4. Based on predictions, what will be the decay factor for annual heart attacks?
Answer: .90
Explanation: Decay factor: (1 - b) = (1-.10) = .90
5. Based on my fictional projections, what will be the percent decrease for strokes in America?
Answer: 5%
Explanation:
A. Choose data for 2 consecutive years: 2010: 7,000,000 strokes; 2011: 6,650,000 strokes
B. Use this formula: Percent decrease = (older – newer)/older
(7,000,000 – 6,650,000)/7,000,000 = .05 or 5%
C. Check for consistency and choose data for another set of consecutive years: 2012: 6,317,500 strokes; 2013: 6,001,625 strokes
Percent decrease = (older – newer)/older
(6,317,500 – 6,001,625)/6,001,625 approximately .05 or 5%
6. Based on my fictional projections, what will be the decay factor for strokes in the America?
Answer: .95
Explanation: Decay factor: (1 - b) = (1-.05) = .95