Answer
a) $p= 2.5+0.03t$
b) $p= 2.5-0.07t$
c) $p(t)=2.5\cdot(1.02)^t$
d) $p(t)=2.5\cdot(0.96)^t$
Work Step by Step
A) The function is linear with a slope of $m= 0.03$. Hence:
$$p= 2.5+0.03t $$
B) The function is linear with a slope of $m= -0.07$. Hence:
$$p= 2.5-0.07t $$
C)
\begin{equation}
\begin{aligned}
r&=2\% = 0.02\\
b&= 1+r= 1.02\\
a&= 2.5\\
\end{aligned}
\end{equation}
The model is
\begin{equation}
\begin{aligned}
p(t)&=2.5\cdot(1.02)^t\\
\end{aligned}
\end{equation}
D)
\begin{equation}
\begin{aligned}
r&=4\% = 0.04\\
b&= 1-r= 0.96\\
a&= 2.5\\
\end{aligned}
\end{equation}
The model is
\begin{equation}
\begin{aligned}
p(t)&=2.5\cdot(0.96)^t\\
\end{aligned}
\end{equation}
