Question

According to the Bureau of the Census, the population of the United States in 1990 was approximately 249 million and in 2000, 281 million. Use this information to predict the population for 2022.

Answer 1

Answer:

The population is predicted to e 367 million in 2022.

Step-by-step explanation:

The population can be modeled by the following equation:

$P(t) = P(0)(1+r)^{t}$

In which P(t) is the population in millions after t years, P(0) is the initial population and r is the growth rate.

1990 was approximately 249 million and in 2000, 281 million.

This means that $P(0) = 249$

2000 is 10 years after 1990, so $P(10) = 281$

So

$P(t) = P(0)(1+r)^{t}$

$281 = 249(1+r)^{10}$

$(1+r)^{10} = \frac{281}{249}$

$(1+r)^{10} = 1.1285$

Applying the tenth root to both sides

$1 + r = 1.0122$

$r = 0.0122$

So

$P(t) = P(0)(1+r)^{t}$

$P(t) = 249(1.0122)^{t}$

Use this information to predict the population for 2022.

2022 - 1990 = 32

So 2022 is 32 years after 1990. We want P(32)

$P(t) = 249(1.0122)^{t}$

$P(32) = 249(1.0122)^{32} = 367$

The population is predicted to e 367 million in 2022.