A wrestler weighed 145 lbs in 1986 and weighs 190 lbs in 2006. What was the rate of change in weight?
Understand the Problem
The question is asking to calculate the average rate of change in weight for a wrestler over a certain time period, specifically from 1986 to 2006. This involves determining the change in weight and dividing it by the number of years over which this change occurred.
Answer
The average rate of change in weight is \(2.25 \, \text{lbs/year}\).
Answer for screen readers
The average rate of change in weight is (2.25 , \text{lbs/year}).
Steps to Solve
- Determine the initial and final weights
The wrestler's weight in 1986 was 145 lbs, and the weight in 2006 was 190 lbs.
- Calculate the change in weight
To find the change in weight, subtract the initial weight from the final weight: $$ \text{Change in weight} = \text{Final weight} - \text{Initial weight} = 190 , \text{lbs} - 145 , \text{lbs} = 45 , \text{lbs} $$
- Calculate the time period
The time period from 1986 to 2006 is: $$ \text{Time period} = 2006 - 1986 = 20 , \text{years} $$
- Calculate the average rate of change in weight
The average rate of change is found by dividing the change in weight by the time period: $$ \text{Average rate of change} = \frac{\text{Change in weight}}{\text{Time period}} = \frac{45 , \text{lbs}}{20 , \text{years}} = 2.25 , \text{lbs/year} $$
The average rate of change in weight is (2.25 , \text{lbs/year}).
More Information
The average rate of change is a useful concept in understanding how a quantity changes over a specific interval, providing insights into trends and patterns.
Tips
- Failing to correctly subtract the initial weight from the final weight.
- Not properly calculating the time period of change.
- Forgetting to divide the change in weight by the number of years to determine the rate.
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