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?
Help me out please!
.97 * .98 * .95 * .98 = .885
or a total decrease of 11.5%
Well, let me take out my trusty calculator and crunch some numbers! If we start with the initial number of smokers and apply the percentage decreases successively, we can calculate the overall percentage decrease.
Let's assume we start with 100 smokers (just to keep the math simple). After the first month, we would have 97 smokers left (100 - 3%). After the second month, we would have 95.06 smokers left (97 - 2%). After the third month, we would have 90.31 smokers left (95.06 - 5%). Finally, after the fourth month, we would have 88.49 smokers left (90.31 - 2%).
Now let's calculate the overall percentage decrease. The equation is (initial - final) / initial * 100. So, it's (100 - 88.49) / 100 * 100 = 11.51%.
So, my number-crunching friend, the overall percentage decrease in the number of smokers over those four months is approximately 11.51%. I hope that helps, and remember, smoking may be going down, but your sense of humor is always on the rise!
To find the overall percentage decrease in the number of smokers during the four-month period, you can follow these steps:
Step 1: Calculate the percentage decrease for each month.
Month 1: The number of smokers decreased by 3%.
Month 2: The number of smokers decreased by 2%.
Month 3: The number of smokers decreased by 5%.
Month 4: The number of smokers decreased by 2%.
Step 2: Calculate the cumulative percentage decrease for all four months.
To calculate the cumulative percentage decrease, you can use the formula:
Cumulative percentage decrease = 1 - ((1 - percentage decrease of month 1) * (1 - percentage decrease of month 2) * (1 - percentage decrease of month 3) * (1 - percentage decrease of month 4))
Plugging in the given values, the formula becomes:
Cumulative percentage decrease = 1 - ((1 - 3%) * (1 - 2%) * (1 - 5%) * (1 - 2%))
Step 3: Simplify the equation and calculate the cumulative percentage decrease.
Cumulative percentage decrease = 1 - (97% * 98% * 95% * 98%)
Cumulative percentage decrease ≈ 1 - 0.97 * 0.98 * 0.95 * 0.98
Calculating the expression, the cumulative percentage decrease is approximately 7.4%.
So, the overall percentage decrease in the number of smokers during the four-month period is about 7.4%.
To calculate the overall percentage decrease in the number of smokers during the four-month period, you need to find the cumulative decrease in the number of smokers.
First, convert the percentage decrease figures to decimals by dividing each percentage by 100.
For the first month: 3% = 0.03
For the second month: 2% = 0.02
For the third month: 5% = 0.05
For the fourth month: 2% = 0.02
Next, calculate the cumulative decrease by multiplying the decimal values.
Cumulative decrease = (1 - 0.03) * (1 - 0.02) * (1 - 0.05) * (1 - 0.02)
Simplifying this equation gives
Cumulative decrease ≈ 0.97 * 0.98 * 0.95 * 0.98
Using a calculator or performing the calculations manually, you get
Cumulative decrease ≈ 0.9230816.
Now, subtract the cumulative decrease from 1 to find the overall percentage decrease.
Overall percentage decrease = (1 - Cumulative decrease) * 100%
Overall percentage decrease ≈ (1 - 0.9230816) * 100%
Calculating this gives
Overall percentage decrease ≈ 7.69%
Therefore, the overall percentage decrease in the number of smokers during the four-month period is approximately 7.69%.