The curve of $y=a{{3}^{bx+2}}-3$ passes through $\left( -1,3 \right)$ and \(\left( 1,51 \right)\

Question

The curve of $y=a{{3}^{bx+2}}-3$ passes through $\left( -1,3 \right)$ and $\left( 1,51 \right)$. Find the values of $a$ and $b$. Hence, sketch the graphs of $y=a{{3}^{bx+2}}-3$, labelling the coordinates of axial intercepts and equations of asymptotes.

Accepted Answer

$a=2$, $b=1$. Intercepts: $(-1-\log_3 2,0)$, $(0,15)$. Horizontal asymptote: $y=-3$.

Finding Unknowns of an Exponential Function

Finding Unknowns of an Exponential Function

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