Choice A is the correct answer. Check the initial value and the multiplier ratio.

1. Initial Value: When $x=0$, $y=5$. So $a=5$. (Eliminates B).
2. Check Ratio: From $x=0$ to $x=1$, $y$ goes $5 \to 15$ ($\times 3$). From $x=1$ to $x=2$, $y$ goes $15 \to 45$ ($\times 3$).
3. Determine Factor: The constant multiplier is 3, so $b=3$.
4. Form Equation: $y = 5(3)^x$.

💡 Strategic Tip: Divide consecutive $y$-values ($y_2 / y_1$) to find the growth factor $b$.

Choice B is incorrect because it has the wrong initial value (3 instead of 5). Choice C is incorrect because$1.3$ is not the correct multiplier. Choice D is incorrect because the growth is not linear (add 10, then add 30).