Question

In 2000, 31% of U.S adults viewed a college education essential for success. For the period 2000-2010, the percentage viewing a college education as essential for success increased on average by approximately 2.4 each year. If trend continues, by which year will 67% of all American adults do the same?
I need the equation please!

Answer 1

$\bf \begin{array}{ccrllll} term&year&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1&2000&31\\ 2&2001&31+2.4\\ 3&2002&(31+2.4)+2.4\\ 4&2003&(31+2.4+2.4)+2.4\\ ...&...&...\\ \boxed{?}&\boxed{?}&67 \end{array} \\ \\ the\ n^{th}\textit{ term of an arithmetic sequence, will be}$$\bf a_n=a_1+(n-1)d\qquad \begin{cases} a_1=\textit{first term}\to 31\\ d=\textit{common difference}\to 2.4\\ n=the\ n^{th}\ term \end{cases} \\ \quad \\ thus \\ \quad \\ a_n=a_1+(n-1)d\implies 67=31+(n-1)2.4$

solve for "n"

the value of the "n"th term is 67, we know that much,
so, "n" will give you how many years it took to be 67