Question

The population of a city in 2005 was 18,000. By 2010, the city’s population had grown to 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

45000-18000=27000
then in.2015
45000+27000=72000 population

Answer 2

Population of the city in 2015 is 112500.

Solution:

To solve the problem we first need to find the growth rate of the population from year 2005 to 2010, we find that by using the formula $\bold{P_{F}=P_{i} e^{R T}}$

$P_{F}$ = Final population or the population of year 2010

$P_{i}$ = Initial population or the population in 2005.

R = Rate of increase of the population  

T = Time taken to see the increase.

Putting the values in $45000=18000 e^{R 5}$

$\frac{45000}{18000}=e^{5 R}$

$2.5=e^{R 5}$, with this we find the population of the year 2015

Now according to the exponential growth method let us find the population in 2015, we use the formula $P_{F}=P_{i} e^{R T}$  

$P_{F}=45000 e^{R 5}=45000 \times 2.5$

Putting the value of $e^{5 R}$  as 2.5 we get $\bold{P_{F}=112500}$