Atmospheric pressure at Earth's surface is approximately 14.7 pounds per square inch. Atmospheric pressure decreases by approximately 16% for each mile increase in height above the surface. Write an exponential equation for the atmospheric pressure P (in pounds per square inch) x miles above Earth's surface.

The exponential equation for the atmospheric pressure P (in pounds per square inch) x miles above Earth's surface can be written as follows:

P = 14.7 * (0.84)^x

Here's how we get this:

1. We start with the atmospheric pressure at Earth's surface, which is 14.7 psi. This is our initial value, or the y-intercept of our equation.

2. We know that the atmospheric pressure decreases by approximately 16% for each mile increase in height above the surface. In other words, the pressure is 84% of what it was for each increase in x (since 100% - 16% = 84%). This is our rate of decrease, or the base of our exponent in our equation.

3. x represents the number of miles above Earth's surface.

So, we multiply the initial pressure by the rate of decrease raised to the power of x to get the pressure at x miles above the surface.