Question

Since the enactment of a smoking ban in a particular​ city, the number of smokers has slowly declined. Statistics show that the number of smokers in this city has decreased for four consecutive months by​ 3%, 2%,​ 5%, and​ 2%. What was the overall percentage decrease in the number of smokers during this four month​ period? Round your answer to the nearest tenth of a percentage point.

Answer 1

The overall percentage decrease in the number of smokers over the four months is calculated through successive percentage decreases, resulting in an approximately 11.5% reduction.

Step-by-step explanation:

To calculate the overall percentage decrease in the number of smokers during this four-month period, we shall apply the successive percentage decrease formula.

1. Let's denote the initial number of smokers as 100%.
2. After a 3% decrease, the number of smokers is 97% of the original number.
3. Then after a further 2% decrease, it becomes 97% - (2% of 97%) = 95.06%.
4. Next, a 5% decrease is applied, which results to 95.06% - (5% of 95.06%) = 90.307%.
5. Finally, after a 2% decrease, the number of smokers becomes 90.307% - (2% of 90.307%) = 88.501%.
6. The overall decrease is 100% - 88.501% = 11.499%, which is approximately 11.5% when rounded to the nearest tenth of a percentage point.

Therefore, the overall percentage decrease in the number of smokers over the four-month period is 11.5%.