Question

The population of a city in 2005 was 18,000. By 2010 the city's population was 45,000. Economists have determined that the population growth follows an exponential model. If they are correct, what is the projected population for 2015?

Answer 1

Answer:

112,547.095  million

Step-by-step explanation:

Data provided in the question

Population of a city in 2005 = 18,000

In the year 2010, the city population = 45,000

Now to find out the projected population for 2015 we use the exponential model

 $P = P(0)\times e^{rt}$

where

P(0) = Initial population

r = growth rate

t = time

e = natural log

So,

$45,000 = 18,000 \times e^{5r}$

So

$e^{5r} = \frac{45}{18}$

$5r = ln \frac{(45)}{(18)}$

r ≈ 0.1833

Now

$P = 18,000e^{10\times0.1833}$

= 112,547.095  million