Answer:
a. [tex]y=2,700(1.04)^x[/tex]
b. 4,322.
Step-by-step explanation:
a. We have been given that the population of a town is 2,700 and is growing 4% each year.
We can see that population of town is increasing exponentially. Since an exponential function is in form: [tex]y=a*b^x[/tex], where,
a = Initial value.
b= For growth b is in form (1+r), where r is rate in decimal form.
[tex]y=a*(1+r)^x[/tex]
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting a=2,700 and r=0.04 we will get,
[tex]y=2,700(1+0.04)^x[/tex]
[tex]y=2,700(1.04)^x[/tex]
Therefore, the equation [tex]y=2,700(1.04)^x[/tex] models the population growth.
b. To find the population after 12 years we will substitute x=12 in our population growth model.
[tex]y=2,700(1.04)^12[/tex]
[tex]y=2,700*1.6010322185676808[/tex]
[tex]y=4,322.78699013273816\approx 4,322[/tex]
Therefore, the population after 12 years will be 4,322.
