We are given a recursive function defined by $a_n = 2a_{n-1}$ with $a_0 = 1$. We need to find the value of $a_3$.

1. Problem Description

We are given a recursive function defined by $a_n = 2a_{n-1}$ with $a_0 = 1$. We need to find the value of $a_3$.

2. Solution Steps

The recursive formula is $a_n = 2a_{n-1}$. We are also given that $a_0 = 1$.

We can use this information to find $a_1$, $a_2$, and finally $a_3$.

For $n=1$, we have:

$a_1 = 2a_{1-1} = 2a_0 = 2(1) = 2$

For $n=2$, we have:

$a_2 = 2a_{2-1} = 2a_1 = 2(2) = 4$

For $n=3$, we have:

$a_3 = 2a_{3-1} = 2a_2 = 2(4) = 8$

3. Final Answer

$a_3 = 8$