A certain city has a population of 30000 and increases by 6% per year. What will the population be 7 years later?
Select one:
a. 42000
b. 45109
c. 156000
d. Over 156000
30000*1.06^7 = ?
To find the population of the city 7 years later, we need to calculate the population growth over that period.
First, let's calculate the increase in population each year. The city's population increases by 6% annually, which means it grows by an additional 6% of the current population every year.
To calculate the growth for each year, we need to multiply the current population by 6% (or 0.06). So, the growth for the first year would be 30,000 * 0.06 = 1,800.
Next, we add the growth to the current population to find the new population after the first year: New population = Current population + Growth = 30,000 + 1,800 = 31,800.
To find the population after the second year, we again calculate the growth by multiplying the current population (31,800) by 0.06: Growth = 31,800 * 0.06 = 1,908.
Adding the growth to the population after the first year gives us: New population = 31,800 + 1,908 = 33,708.
We repeat this process for each subsequent year:
Year 3: New population = 33,708 + (33,708 * 0.06) = 35,762.8 (approximately).
Year 4: New population = 35,762.8 + (35,762.8 * 0.06) = 37,935.048 (approximately).
Year 5: New population = 37,935.048 + (37,935.048 * 0.06) = 40,235.0448 (approximately).
Year 6: New population = 40,235.0448 + (40,235.0448 * 0.06) = 42,668.696288 (approximately).
Year 7: New population = 42,668.696288 + (42,668.696288 * 0.06) = 45,242.66144928 (approximately).
The population of the city after 7 years will be approximately 45,242.66144928.
Among the options provided, the closest value to the calculated population is option b. 45109. Therefore, the correct answer is b. 45109.