$8000 is borrowed, and I'm assuming that 19% is our rate of interest and we want to make an equation to show how much is owed at any point in time.
A typical exponential equation follows this format:
[tex]y = a(b)^{x} [/tex]
"b" in this case is the rate at which our debt is changing. If "b" is 1, that means that our debt is stagnant and neither increasing not decreasing. If "b" is less than 1, it means that our debt is being paid off or forgiven at a certain rate. If "b" is more than 1, our debt is constantly getting larger.
In our case, our debt is increasing since interest is a process that "punishes" you by charging you a percentage of what you borrowed, then charging you a percentage of the new debt from that and so on. It is said that interest charges you "money on money"- unfair if you ask me.
Since our debt is increasing by 19%, when we plug this interest into our generic equation we'll have to make it so that we have our original debt and our interest rate. 1.19 will give us what we need (original 100%+ 19% interest is the same as 1+.19).
Okay, now our equation should look like
[tex]y = a(1.19)^{x} [/tex]
"a" is our last needed variable. "a" stands for our initial debt (our initial value). We already know this, it's $8000.
So now, our final equation would be
[tex]y = 8000 ({1.19})^{x} [/tex]
