So for this, we will be creating an equation using the exponential formula - which is [tex]y=ab^x[/tex] (a = initial value, b = growth/decay).
Firstly, we know that the original population of the deer is 1,500 so that will be our a value.
Next, we know that the population is growing by 2% annually. With this, we will add 1 and 0.02 (2% in decimal form) since the population is increasing.
1.02 will be our b variable. Now putting it together, our equation is: [tex]y=1500(1.02)^x[/tex]
Now that we have our equation set up, plug 4 into the x variable and solve for y as such (Remember to not round until the very end):
[tex]y=1500*(1.02)^4\\y\approx 1624[/tex]
After 4 years, the deer population will be 1,624.
