Oil prices have increased a great deal in the last decade. The following table shows the average oil price for each year since $1949.$ Many companies use oil products as a resource in their own business operations $($like airline firms and manufacturers of plastic products$).$ Managers of these firms will keep a close watch on how rising oil prices will impact their costs. The interest rate in the PVIFV equations can also be interpreted as a growth rate in sales, costs, profits, and so on$.$

$\backslash$table$[[$Average Oil Prices$],[$Year$,\backslash$table$[[$per$],[$barrel$]],$Year,per barrel,Year,per,barrel,Year,per,barrel$],[1949,$$$2\mathrm{.}54,1969,$$$3\mathrm{.}09,1989,$$$,15\mathrm{.}86,2009,$$$,53\mathrm{.}48],[1950,$$$2\mathrm{.}51,1970,$$$3\mathrm{.}18,1990,$$$,20\mathrm{.}03,2010,$$$,71\mathrm{.}21],[1951,$$$2\mathrm{.}53,1971,$$$3\mathrm{.}39,1991,$$$,16\mathrm{.}54,2011,$$$,87\mathrm{.}04],[1952,$$$2\mathrm{.}53,1972,$$$3\mathrm{.}39,1992,$$$,15\mathrm{.}99,2012,$$$,93\mathrm{.}02],[1953,$$$2\mathrm{.}68,1973,$$$3\mathrm{.}89,1993,$$$,14\mathrm{.}25,2013,$$$,97\mathrm{.}91],[1954,$$$2\mathrm{.}78,1974,$$$6\mathrm{.}87,1994,$$$,13\mathrm{.}19,2014,$$$,93\mathrm{.}26],[1955,$$$2\mathrm{.}77,1975,$$$7\mathrm{.}67,1995,$$$,14\mathrm{.}62,2015,$$$,48\mathrm{.}69],[1956,$$$2\mathrm{.}79,1976,$$$8\mathrm{.}19,1996,$$$,18\mathrm{.}46,2016,$$$,43\mathrm{.}14],[1957,$$$3\mathrm{.}09,1977,$$$8\mathrm{.}57,1997,$$$,17\mathrm{.}23,2017,$$$,50\mathrm{.}88],[1958,$$$3\mathrm{.}01,1978,$$$9\mathrm{.}00,1998,$$$,10\mathrm{.}87,2018,$$$,65\mathrm{.}23],[1959,$$$2\mathrm{.}90,1979,$$$12\mathrm{.}64,1999,$$$,15\mathrm{.}56,2019,$$$,56\mathrm{.}99],[1960,$$$2\mathrm{.}88,1980,$$$21\mathrm{.}59,2000,$$$,26\mathrm{.}72,2020,$$$,39\mathrm{.}23],[1961,$$$2\mathrm{.}89,1981,$$$31\mathrm{.}77,2001,$$$,21\mathrm{.}84,,,],[1962,$$$2\mathrm{.}90,1982,$$$28\mathrm{.}52,2002,$$$,22\mathrm{.}51,,,],[1963,$$$2\mathrm{.}89,1983,$$$26\mathrm{.}19,2003,$$$,27\mathrm{.}54,,,],[1964,$$$2\mathrm{.}88,1984,$$$25\mathrm{.}88,2004,$$$,38\mathrm{.}93,,,],[1965,$$$2\mathrm{.}86,1985,$$$24\mathrm{.}09,2005,$$$,46\mathrm{.}47,,,],[1966,$$$2\mathrm{.}88,1986,$$$12\mathrm{.}51,2006,$$$,58\mathrm{.}30,,,],[1967,$$$2\mathrm{.}92,1997,$$$15\mathrm{.}40,2007,$$$,64\mathrm{.}67,,,],[1968,$$$2\mathrm{.}94,1988,$$$12\mathrm{.}58,2008,$$$,91\mathrm{.}48,,,]]$

a$.$ Using the $1949$ oil price and the $1969$ oil price, compute the annual growth rate in oil prices during those $20$ years.

b$.$ Compute the annual growth rate between $1969$ and $1989$ and between $1989$ and $2020.$

c$.$ Given the price of oil in $2020$ and your computed growth rate between $1989$ and $2020,$ compute the future price of oil in $2023$ and $2028.$

Note: Round your answer to $2$ decimal places.