Question

Multiple Choice Which of the following gives the best approximation for the zero of \(f(x)=4-e^{x} ?\) (A) \(x=-1.386 \quad\) (B) \(x=0.386 \quad\) (C) \(x=1.386\) (D) \(x=3 \quad\) (E) there are no zeros

Short answer

The best approximation for the zero of the provided function is (C) \(x=1.386\).

Step-by-step solution

Set f(x) to Zero

To find the zero of the function, set the function \(f(x) = 4 - e^{x}\) equal to 0. This gives us an equation \(4 - e^{x} = 0\).

Solve for x

To solve for \(x\), rearrange the equation, giving \(e^{x} = 4\). Taking the natural logarithm on both sides, we get \(x = ln(4)\). Calculate the value of \(x\), which is approximately 1.386.

Compare with the Given Options

After evaluating, our result for \(x\) is approximately 1.386. Comparing this with the available answers, we find that the correct option is (C) \(x=1.386\).