Final answer:
To estimate the population of the U.S. in 2000 from a 1970 population of 203 million growing at 3% per year, the exponential growth formula gives an estimated population of roughly 499 million in 2000.
Step-by-step explanation:
The estimated population growth of the United States can be calculated using the formula for exponential growth, which is P(t) = P0 * e^(rt), where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in years. Using the given data, the initial population (P0) in 1970 was 203 million, the growth rate (r) is 3%, or 0.03 when expressed as a decimal, and the time (t) from 1970 to 2000 would be 30 years.
Plugging in these values, we get:
P(30) = 203 million * e^(0.03 * 30)
= 203 million * e^(0.9)
Using a calculator, we can find e^(0.9) ≈ 2.46
Thus, the estimated population in the year 2000 would be roughly:
P(30) = 203 million * 2.46 ≈ 499.38 million
Therefore, the estimated population of the United States in the year 2000 would be approximately 499 million.