Answer:
[tex]y=9,800*1.02^x;about\text{ 11,257 people}[/tex]
Explanation:
Given:
Initial population(a) = 9800
Rate of increase in decimal(r) = 2% = 2/100 = 0.02
Time period(x) = ?
To find:
Equation model and population after 7 years
Recall the below exponential growth function;
[tex]y=a*(1+r)^x[/tex]
Let's go ahead and substitute the given value into the above to have the equation that models the population growth;
[tex]\begin{gathered} y=9800*(1+0.02)^x \\ y=9800*1.02^^x \end{gathered}[/tex]
When x = 7, let's go ahead and solve for y;
[tex]\begin{gathered} y=9800*1.02^7 \\ y=9800*1.14868566765 \\ y=11,257 \end{gathered}[/tex]
So the population after 7 years will be 11,257 people
