In 2000, the population of a town was 8914. the population is expected to grow at a rate of 1.36% each year. what is the population of the town in 2006? round the answer to the nearest whole number.

9667

Step-by-step explanation:

The population is 8914 in 2000. We must exlude the growth in 2000. Therefore, the population grows for 6 years. We can write an expression for the population growth. The growth rate applies to the total population of the previous year. So for year 2001 the population will be:

So for 2002 we will take 2001 population and multiply it by the growth rate and add 2001 population to get 2002 total population:

For 2003:

For 2004:

For 2005:

For 2006:

The population in 2006 is 9667

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!