Chapter 3.1, Problem 34E

To determine

To find: The value of the function $f\left(x\right)$ for the given value of x .

Answer to Problem 34E

The value of the function $f\left(x\right)=1.5e^{\frac{x}{2}}$ when $x=240$ is $1.956$ .

Explanation of Solution

Given information:

The function $f\left(x\right)=1.5e^{\frac{x}{2}}$ and x -value $x=240$ .

Formula used:

Substitute the provided value of the variable in the function to estimate the value.

Calculation:

Consider the provided function $f\left(x\right)=1.5e^{\frac{x}{2}}$ and x -value $x=240$ .

Substitute x as $240$ in the above equation,

  $\begin{array}{l}f\left(240\right)=1.5e^{\frac{240}{2}}\\ f\left(240\right)=1.5e^{120}\end{array}$

Use the calculator key strokes, $1.5$ then $\boxed{e^x}$ then $\boxed{(-)}$ $120$ and last press the $\boxed{\text{ENTER}}$ key.

The result obtained on display screen is, $1.95627132\times {10}^{52}$ .

Round off the result obtained to three decimal places $1.956$ .

Hence, the value of the function $f\left(x\right)=1.5e^{\frac{x}{2}}$ when $x=240$ is $1.956$ .