## Algebra 2 Common Core

The function represents exponential decay and the y-intercept is at $(0,10).$
In order to determine whether this graph represents exponential growth or exponential decay, we must first remember that exponential growth and decay functions look like this: $y = a(b)^{x}$ $a$ = y-intercept $b$ = Rate of growth/decay If b is between $0$ up to but not including $1$, the function is exponential decay. If b is greater than $1$, the function is exponential growth. In this case, $b = 0.45$, which is less than $1$, which means that the function represents exponential decay. To find the Y-intercept, we plug in $0$ for $x$. $y = 10(0.45)^0 = 10(1) = 10$ The y-intercept is $(0,10)$.