Final answer:
Using the exponential growth formula and plugging in the given values, we calculate that the city's population will reach 1 million in approximately 15 years, making option B) In 15 years the correct answer.
Step-by-step explanation:
To determine when the population of a city, which is 475,000 and increasing by 3.75% each year, will reach 1 million, we can use the formula for exponential growth: P = P0(1 + r)^t, where P is the future population, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, P0 is 475,000, r is 0.0375, and we want to solve for t when P equals 1,000,000.
By rearranging the formula and solving for t, we get: t = ln(P/P0) / ln(1 + r). Plugging in the values, we get: t = ln(1,000,000/475,000) / ln(1.0375). After calculating, this gives us a value for t which we can compare to the options provided in the question.
After performing the calculation, we find that the time t is approximately 15 years. Therefore, the correct answer is B) In 15 years.