A certain city has a population of 200,000. If the population decreases by 10% e

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Question: A certain city has a population of 200,000. If the population decreases by 10% every year, what will be the population after 3 years?

Options:

Correct Answer: 162,000

Solution:

Population after 3 years = 200,000 * (1 - 0.10)^3 = 200,000 * 0.729 = 145,800.

A certain city has a population of 200,000. If the population decreases by 10% every year, what will be the population after 3 years?

A certain city has a population of 200,000. If the population decreases by 10% every year, what will be the population after 3 years?

Step 1: Start with the initial population of the city, which is 200,000.
Step 2: Understand that a 10% decrease means the population will be 90% of the current population each year.
Step 3: Convert 90% to a decimal. 90% is the same as 0.90.
Step 4: To find the population after 1 year, multiply the initial population by 0.90: 200,000 * 0.90.
Step 5: Calculate the population after 1 year: 200,000 * 0.90 = 180,000.
Step 6: Repeat the process for the second year. Multiply the population after 1 year (180,000) by 0.90: 180,000 * 0.90.
Step 7: Calculate the population after 2 years: 180,000 * 0.90 = 162,000.
Step 8: Repeat the process for the third year. Multiply the population after 2 years (162,000) by 0.90: 162,000 * 0.90.
Step 9: Calculate the population after 3 years: 162,000 * 0.90 = 145,800.

Exponential Decay – The question tests the understanding of exponential decay, where a quantity decreases by a constant percentage over time.
Percentage Calculation – It requires the ability to calculate percentages and apply them to a population figure.
Compound Interest Formula – The formula used is similar to the compound interest formula, where the population is multiplied by a factor raised to the power of time.