Answer
No.
Explanation given below.
Work Step by Step
Graphing the model function $P(t)$, we note that for the first $13$ years, the price of oil decreased to a value of ${{\$}} 25 $ per barrel in $1980+13=1993$.
It then increased to about ${{\$}} 97.2$ in $2006$.
So, it is not true that the price hardly changed over these years.