Pharmacist John S$.$ Pemberton invented a soft drink in $1886$ that eventually became not only an integral part of everyday life in the United States but

also a symbol of consumerism worldwide. In $1929$ the first Coca$-$Cola vending machines were installed in Germany, and in $1930,$ the German branch

of the Coca$-$Cola Co$.$ opened in Essen.

Coca$-$Cola sales in Germany were $243,000$ cases in $1934,1$ million cases in $1936,$ and $4\mathrm{.}5$ million cases in $1939.$

Germany was a growing market for Coca$-$Cola, along with other countries in Europe, before World War II$.$ With the previous data given, calculate the

company's sales growth rate for each time period in the following table:

Coca$-$Cola's worldwide sales as of December $31,2011,$ was $26\mathrm{.}7$ billion cases. Assume the following sales distribution:

If Coca$-$Cola's worldwide growth were to continue at the same growth rate as it did in Germany between $1939$ and $2008,$ when sales grew at the rate

of $10\mathrm{.}26\%,$ its hypothetical sales in France in $2053(42$ years from $2011)$ would be approximately

billion cases. $($Note: For this question,

ignore other factors that affect sales.$)$