Problem $4-26$ Spreadsheet Problem: Growth Rates $($LG$4-7)$

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 PV$/$FV equations can also be interpreted as a growth rate in sales, costs, profits, and so on$.$

$\backslash$table$[[$Average $0$ Oil Prices,$],[,$per$],[$Year$,$barrel,Year,$\backslash$table$[[$per$],[$barrel$]],$Year,$\backslash$table$[[$per$],[$barrel$]],$Year,$\backslash$table$[[$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.