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label Mathematics
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The following is a partial table of values for 

f = f(x).
x
f = f(x)
05.1
54.1
101.9
153.9
207.1
Calculate the average rate of change from 
x = 10
 to 
x = 15.
 
 

Use your answer to estimate the value of 
f(13).
 (Round your answer to one decimal place.) 
Sep 3rd, 2015

Hello!

The average rate of change is dy/dx (the change of the function divided by the change of x).
Here it is

(-3.9 - 1.9)/(15 - 10) = -5.8/5 = -11.6/10 = -1.16.

To estimate f(13) we suppose f(x) is linear between x=10 and x=15.
Then f(13) approx = f(10) + (dx from 10 to 13) * (the average rate). Substitute our numbers:

f(13) approx = f(10) + (13-10)*(-1.16) = 1.9 - 3*1.16 = 1.9 - 3.48 = -1.58 approx = -1.6

Please ask if anything is unclear.
Sep 3rd, 2015

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