If the population of a city increases by 5% in the time interval (time expressed in years) from t=0 to t=1, and the population increases by 8% in the time interval from t=1 to t=2, then find the population growth between t=0 and t=2.

1. A

   13%

2. B

   13.8%

3. C

   13.4%

4. D

   14.2%

Appeared in: CGHS SSC - 2018

Explanation

• The problem involves two consecutive percentage increases, which means the growth compounds.
• The first increase of 5% is applied to the initial population.
• The second increase of 8% is applied to the new, larger population after the first year's growth.
• Let the initial population be P. After 1 year, it is P(1.05). After the second year, it is P(1.05)(1.08) = P(1.134).
• The total growth is 1.134 - 1 = 0.134, which is equivalent to a 13.4% increase from the original population.

Why Other Options Were Wrong

• Option A: This is the result of incorrectly adding the two percentages (5% + 8% = 13%). This method is wrong because it ignores the compounding effect; the 8% growth in the second year is on a larger base population.
• Option B: This value is a result of a calculation error. It does not correspond to the correct method of calculating successive percentage change.
• Option D: This value is a result of a calculation error. It does not correspond to the correct method of calculating successive percentage change.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Percentage Change as background academic context rather than a clinical decision trigger.
• Understanding compound growth is essential in public health and epidemiology for tracking population statistics, disease prevalence, and incidence rates over time.
• Nurses and healthcare planners use these calculations to project future healthcare needs, such as the number of hospital beds, vaccines, or specialized services required for a growing or aging population.
• What if? - If the population had decreased by 5% in the first year and then increased by 8% in the second, the calculation would be P(1 - 0.05)(1 + 0.08) = P(0.95)(1.08) = P(1.026). The net growth would be 2.6%.

How to Approach the Question

• First, identify that the question describes two consecutive percentage changes over different time periods. This indicates a successive percentage change or compound growth problem.
• Recognize the common trap: do not simply add the percentages (5% + 8% = 13%). The base for the second percentage change is different from the initial base.
• Choose a simple initial value, like 100, to make calculations easier. Calculate the value after the first percentage change.
• Apply the second percentage change to the new value obtained in the previous step.
• Calculate the total change from the original value and express it as a percentage.
• Alternatively, use the formula for successive percentage change: (a + b + ab/100)%, where 'a' and 'b' are the percentage changes.

Concept Tested & Keywords

• Concept Tested: Successive Percentage Change
• Stem keywords: population, increases by 5%, increases by 8%, population growth
• Lead-in keywords: find
• Negative lead-in flag: false

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QAFUp-qaXhOeaLFOnL4IXY

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