Question

the 2020 census found a u.s. population of about 330 million. starting from this value, use the current u.s. annual growth rate of 0.6% (which includes immigration as well as births and deaths) to estimate u.s. population in 2054 and 2095. use the approximate doubling time formula.

what is the predicted population in 2054?
404 million
(round to the nearest whole number as needed.)

what is the predicted population in 2095?
million
(round to the nearest whole number as needed.)

Explanation:

Calculate the doubling time

Using the Rule of 70 and Doubling Time concepts, we find the approximate doubling time \(T_{\text{double}}\) for a growth rate of \(r = 0.6\%\):

$$ T_{\text{double}} \approx \frac{70}{r} = \frac{70}{0.6} \approx 116.67 \text{ years} $$

Determine the population in 2095

Using the Population Trend Prediction concept, we calculate the number of years \(t\) from the 2020 base year to 2095:

$$ t = 2095 - 2020 = 75 \text{ years} $$

Using the exponential growth formula with the doubling time:

$$ P(t) = P_0 \times 2^{t / T_{\text{double}}} $$

Substitute \(P_0 = 330\) million, \(t = 75\), and \(T_{\text{double}} = \frac{70}{0.6}\):

$$ P(75) = 330 \times 2^{75 / 116.67} \approx 330 \times 2^{0.642857} \approx 330 \times 1.56139 \approx 515.26 \text{ million} $$

Rounding to the nearest whole number gives \(515\) million.

Answer:

What is the predicted population in 2095?
<blank>515</blank> million
(Round to the nearest whole number as needed.)