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The function f(x)= -45x + 270 represents the total distance, in miles, a traveler is from home x hours after beginning the trip home. What is the average rate of change over the interval from x = 1 to x = 3, in miles per hour?

User ReynierPM
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1 Answer

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\bold{\huge{\underline{ Solution }}}

Given :-

  • We have given one function f(x) = -45x + 270
  • The given function represents the total distance in miles.
  • The initial interval was x = 1 and final interval was x = 3

To Find :-

  • We have to find the rate of change over the given interval

Let's Begin :-

Here, We have

  • Function = f(x) = -45x + 270

The given function represents the total distance in miles covered by the traveller.

Therefore,

For initial interval that is x = 1 , Distance covered by the traveller


\sf{ f(x) = -45x + 270 }


\sf{ f(1) = - 45(1) + 270 }


\sf{ f(1) = - 45 + 270 }


\sf{ f(1) = 225 }

For final interval that is x = 3, Distance covered by the traveller


\sf{ f(x) = - 45x + 270 }


\sf{ f(1) = - 45(3) + 270 }


\sf{ f(1) = - 135 + 270 }

Now,

We have to find the average rate of change over the given time interval

Therefore,

Average rate of change in the given time interval


\sf{ = }{\sf{( f(1) + f(3) )/(3 - 1)}}


\sf{ = }{\sf{( 225 + ( -135) )/( 2)}}


\sf{ = }{\sf{( 225 - 135 )/( 2)}}


\sf{ = }{\sf{( 90 )/( 2)}}


\sf{ = 45 }

Hence, The average rate of change over the given interval is 45 miles per hour.

User Vitali Kaspler
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