Chapter 6.3, Problem 53E

(a)

To determine

To calculate: The speed of the wind near the center of the tornado.

Answer to Problem 53E

The required speed of the tornado is $282.8\text{miles}\text{per}\text{hour}$ .

Explanation of Solution

Given information:

The expression for the speed is $s=93\log d+65$ .

Distance traveled by the tornado $=220\text{miles}$

Calculation:

Consider the expression for the speed is $s=93\log d+65$ .

Find the speed of the tornado.

Substitute the value 220 for $d$ .

  $\begin{array}{c}s=93\times \log 220+65\\ =282.8453\dots \\ \approx 282.8\text{miles}\text{per}\text{hour}\end{array}$

Hence, the required speed of the tornado is $282.8\text{miles}\text{per}\text{hour}$ .

(b)

To determine

To calculate: The inverse of the function.

Answer to Problem 53E

The required inverse of the function is $d={10}^{\frac{s-65}{93}}$ .

Explanation of Solution

Given information:

The expression for the speed is $s=93\log d+65$ .

Calculation:

The given expression for the speed is $s=93\log d+65$ .

Rewrite the expression as

  $\begin{array}{c}s-65=93\log d\\ \log d=\frac{s-65}{93}\end{array}$

Convert the logarithmic form into exponential form.

Since the given logarithmic function is in common log form. Thus, the base of the log is 10.

Take exponential in each side with base 10.

  $\begin{array}{c}\log d=\frac{s-65}{93}\\ {10}^{\log d}={10}^{\frac{s-65}{93}}\\ d={10}^{\frac{s-65}{93}}\end{array}$

Hence, the required inverse of the function is $d={10}^{\frac{s-65}{93}}$ .