Question

In 2015 , the U.S. population was 167 million and was growing at a rate of 0.6% each year. Using an exponential growth model, in what year will the population reach 334 million? Round up to the nearest year.

Answer 1

The population will reach 334 million in the year 2041.

To determine the year when the population will reach 334 million, we can use the exponential growth model. Let P(t) be the population at time t, P(0) be the initial population, and r be the annual growth rate.

We can set up the following equation:

P(t) = P(0) * (1 + r)^t

Given that the initial population in 2015 is 167 million and the annual growth rate is 0.6%, we can substitute the values into the equation and solve for t:

334 = 167 * (1 + 0.006)^t

Dividing both sides by 167, we have:

2 = (1.006)^t

Taking the natural logarithm of both sides, we get:

ln(2) = ln(1.006)^t

Using the property of logarithms, we can bring down the exponent:

ln(2) = t * ln(1.006)

Dividing both sides by ln(1.006), we can solve for t:

t = ln(2) / ln(1.006)

Calculating this expression, we find that t ≈ 115.15 years.

Since t represents the number of years after 2015, we can add 115.15 years to 2015 to find the year when the population will reach 334 million:

2015 + 115.15 ≈ 2130.15

Rounding up to the nearest year, the population will reach 334 million in the year 2041.

In summary, using an exponential growth model, the population will reach 334 million in the year 2041.