Final answer:
To find the population of a city two years ago with a current population of 490,000 increasing at 12% per annum, the formula P0 = P / (1 + r)n is used. The calculated initial population is approximately 390,625, which does not match any of the given options.
Step-by-step explanation:
The question asks to find the population of a city two years ago given that the current population is 490,000 and it increases at a rate of 12% per annum. To calculate the population two years prior, we need to reverse the growth. We use the formula for exponential growth P = P0 (1 + r)n, where P is the final population, P0 the initial population, r the rate of growth, and n the number of time periods.
To find the initial population (two years ago), we solve for P0: P0 = P / (1 + r)n. Substituting for P = 490,000, r = 0.12, and n = 2, we get:
P0 = 490,000 / (1 + 0.12)2 = 490,000 / (1.12)2 = 490,000 / 1.2544 = 390,625 (approximately)
None of the options a) 436,480 b) 435,600 c) 430,240 d) 423,120 match the calculated value of 390,625. Therefore, there may be an error either in the question or the provided options.