Question

The 1970 census estimated the population of the United States to be 203 million. If this population grew at the rate of 3% per year, what population will there be approximately in the year 2000? Please calculate the estimated population in the year 2000.

Answer 1

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.