Chapter 1.3, Problem 46E

To determine

Tofind:The correct option of the approximation for the zero of the function $f\left(x\right)=4-e^x$ .

Answer to Problem 46E

The correct option is (C) as the zero of the function $f\left(x\right)=4-e^x$ is $x=1.386$ .

Explanation of Solution

Given information:The function is $f\left(x\right)=4-e^x$ .

Calculation:

To get the zero of the function equate it to zero.

  $\begin{array}{c}f\left(x\right)=0\\ 4-e^x=0\\ e^x=4\end{array}$

Take logarithm to both the sides of above equation and solve.

  $\begin{array}{c}\ln e^x=\ln 4\\ x\ln e=1.386\\ x=1.386\end{array}$

Therefore, the correct option is (C) as the zero of the function $f\left(x\right)=4-e^x$ is $x=1.386$ .