The resident population of the United States in 2019 was 329 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 329(1.007)^t−2019 represents the population P (in millions of people) in year t.

(a) According to this model, when will the population of the United States be 415 million people?

(b) According to this model, when will the population of the United States be 470 million people?