Integer-base exponential graphs

In \(y=ka^x\), the base \(a\) is a positive integer. For \(a>1\) and \(k\ne0\), each increase of \(1\) in \(x\) multiplies \(y\) by \(a\). The \(y\)-intercept is \((0,k)\), because \(a^0=1\). The graph approaches the horizontal axis as \(x\) becomes increasingly negative.

Example

For \(y=2(3^x)\), the outputs at \(x=-1,0,1,2\) are \(\dfrac23,2,6,18\). It is multiplication by \(3\), not addition of \(3\), at each step.

For positive \(k\) the curve increases and stays positive; for negative \(k\) it decreases and stays negative. If \(a=1\), the graph is the constant line \(y=k\). If \(k=0\), it is \(y=0\).

To estimate the input for a specified output, draw a horizontal reading line to the curve and read down to the input axis. State only the accuracy supported by the graph.