Exercise 9.
Let
\begin{equation*} f(x)=\begin{cases} \ln(2x)&x \le 50\\ 200\exp(-x/10)&x \gt 50\\ \end{cases}\text{.} \end{equation*}
Solution.
  1. The Excel command is =IF(A2 < =50, LN(2*A2),200*EXP(-A2/10))
  2. The chart is produced by the following code.
  3. The graph will look as follows. Note that the function is not defined at 0.
  4. The function is not continuous at \(x = 50\text{.}\) Note that the function drops from near 4.5 to about 1 rather suddenly.
in-context