Question

a particular city had a population of 24,000 in 1900 and a population of 29,000 in 1920. Assuming that its population continues to grow exponentially at a constant rate, what population will it have in 2000

Answer 1

Answer:

It will have a population of 61,779 in 2000.

Step-by-step explanation:

The population for the city, in t years after 1900, can be modeled by a exponential function with constant growth rate in the following format:

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

In which P(0) is the population in 1900 and r is the growth rate.

Population of 24,000 in 1900

This means that $P(0) = 24000$

Population of 29,000 in 1920.

1920 is 1920 - 1900 = 20 years after 1900.

This means that P(20) = 29000. So

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

$29000 = 24000(1+r)^{20}$

$(1+r)^{20} = \frac{29000}{24000}$

$\sqrt[20]{(1+r)^{20}} = \sqrt[20]{\frac{29000}{24000}}$

$1 + r = 1.0095$

So

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

$P(t) = 24000(1.0095)^{t}$

What population will it have in 2000

2000 is 2000 - 1900 = 100 years after 1900. So this is P(100).

$P(t) = 24000(1.0095)^{t}$

$P(100) = 24000(1.0095)^{100} = 61779$

It will have a population of 61,779 in 2000.