Integer-base exponential graphs

The prescribed family is \(y=ka^x\), where \(a\) is a positive integer and \(k\) is a constant. In the examples here, \(k>0\). Whenever \(x\) increases by 1, the value of \(y\) is multiplied by \(a\). For an integer \(a>1\), the graph rises; when \(a=1\), it is constant.

Both graphs pass through \((0,1)\), remain positive, and approach the \(x\)-axis as \(x\) becomes increasingly negative. These diagrams have different vertical scales; use the axis numbers when comparing values.

To estimate an input from an output, draw a horizontal line to the smooth curve, then read vertically down to the \(x\)-axis. Joining two points by a straight line generally gives a different estimate.