Question

The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.

Answer 1

a) 207 mph

b) x = (1260-w)/1.17

c) 1000 mb

Explanation:

a) Put the pressure in the equation and solve.

w(900) = -1.17(900) +1260 = 207

The wind speed for a hurricane with a pressure of 900 mb is 207 mph.

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b) Solving for x, we have ...

w = -1.17x +1260

w -1260 = -1.17x

x = (1260 -w)/1.17 . . . . inverse function

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c) Evaluating the inverse function for w=90 gives ...

x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars

The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.