The problem provides a function $f(x) = 93\log d + 65$ that relates the speed of the wind, $f(x)$, in miles per hour near the center of a tornado to the distance $d$ that a tornado travels in miles. Given that a tornado has sustained winds of 400 mph, we need to estimate the distance it can travel.

1. Problem Description

The problem provides a function $f(x) = 93\log d + 65$ that relates the speed of the wind, $f(x)$, in miles per hour near the center of a tornado to the distance $d$ that a tornado travels in miles. Given that a tornado has sustained winds of 400 mph, we need to estimate the distance it can travel.

2. Solution Steps

We are given the function $f(x) = 93\log d + 65$ and $f(x) = 400$. We need to solve for $d$.

$400 = 93\log d + 65$

Subtract 65 from both sides:

$400 - 65 = 93\log d$

$335 = 93\log d$

Divide by 93:

$\frac{335}{93} = \log d$

To solve for $d$, we need to use the property that if $\log d = x$, then $d = 10^x$.

$d = 10^{\frac{335}{93}}$

$d \approx 10^{3.602}$

$d \approx 4000$

3. Final Answer

4000 miles