Hi There!
Find the population in 3 years.
8,200 x 0.03 = 246
8,200 + 246 = 8,446
8,446 x 0.03 = 253.38
8,446 + 253.38 = 8,699.38
8,699.38 x 0.03 = 260.9814
8,699.38 + 260.9814 = 8,960.3614
Round: 8,960.3614 = 8,960
Answer: y = 8,200 ∙ 1.03x; about 8,960 people
Hope This Helps :)
Answer:
Option 4th is correct
[tex]y = 8200(1.03)^t[/tex]
about 8,960 people
Step-by-step explanation:
Using the formula:
[tex]y=a(1+r)^t[/tex] .....[1]
where
[tex]a[/tex] is the initial population.
r is the growth rate in decimal
y is the population after t years.
As per the statement:
Suppose the population of a town is 8,200 and is growing 3% each year.
⇒[tex]a = 8200[/tex] and r = 3% = 0.03
Substitute the given values in [1] , we have;
[tex]y = 8200(1+0.03)^t[/tex]
⇒[tex]y = 8200(1.03)^t[/tex] .....[2]
Now, we have to find the population after 3 years.
Put t = 3 years in [2] we have;
[tex]y = 8200(1.03)^3[/tex]
⇒[tex]y = 8200 \cdot 1.092727[/tex]
⇒[tex]y =8960.3614[/tex]
Therefore, an equation to model the population growth is,
[tex]y = 8200(1.03)^t[/tex] ; and
The population after 3 years about 8,960 people
