Question

find equation for exponential relationship whose graph passes through each pair of points a)(1,6) and (2,12) b) (2,90) and (4,810)

Answer 1

\(\large\color{slate}{ y=a(b)^x }\) is an equation of an(y) exponential function.

where
\(\large\color{slate}{ b>0 }\)
\(\large\color{slate}{ a \in {\bf R} }\)


`Notations if you don't know them.`
\(\large\color{blue}{ {\bf R} }\) is a notation that denotes "all real numbers"
(saying that \(\large\color{blue}{ {\bf R} }\) is a notation for (a set of) ALL REAL NUMBERS)
and \(\large\color{blue}{ \in }\) means "belongs to a set of".
So, \(\large\color{blue}{ a \in {\bf R} }\) means "a belongs to a set of real numbers" i.e. \(\large\color{slate}{ \color{blue}{ a } }\) can be any real number.

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to find "a" and "b" use this format with both of the points (1,6) and (2,12) .

\(\large\color{slate}{ y=a(b)^x }\)

the system you need to solve is:
\(\large\color{slate}{ 6=a(b)^1 }\)
\(\large\color{slate}{ 12=a(b)^2 }\)