Answer:
To find an explicit formula for \( p_n \), we can derive it from the recursive rule given.
Given:
- \( p_0 = 1.3 \) billion
- \( p_n = p_{n-1} + 2 \)
Let's express \( p_n \) in terms of \( n \) using the recursive rule:
\[
\begin{align*}
p_1 &= p_0 + 2 = 1.3 + 2 \\
p_2 &= p_1 + 2 = (p_0 + 2) + 2 = 1.3 + 2 + 2 \\
p_3 &= p_2 + 2 = ((p_0 + 2) + 2) + 2 = 1.3 + 2 + 2 + 2 \\
\vdots \\
p_n &= p_0 + 2n = 1.3 + 2n
\end{align*}
\]
So, the explicit formula for \( p_n \) is \( p_n = 1.3 + 2n \) billion dollars.
