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Sagot :
a. The average rate of change of the function f(x)= [tex]120(0.1)^x[/tex] from x = 0 to x = 2 is
b. The average rate of change of the function f(x)= [tex]4(2)^x[/tex] from x = 0 to x = 2 is
c. The average rate of change of the function f(x)= [tex]480(0.3)^x[/tex] from x = 1 to x = 5 is
The average rate of change of the function is given by-
[tex]\frac{f(1)-f(0)}{1-0}[/tex]
Now, apply the same to all the given functions to find the average rate of change of the functions as follows.
a. The given function is f(x) = [tex]120(0.1)^x[/tex]
We have to find the average rate of change of this function from x = 0 to x = 2
The average rate of change = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= (120 [tex](0.1)^2[/tex] - 120) / 2
= 60 (0.01 - 1)
= 60 x - 0.99 = - 59.4
Thus, the average rate of change = - 59.4
b. The given function is f(x) = [tex]4(2)^x[/tex]
We have to find the average rate of change of this function from x = 0 to x = 2
The average rate of change = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= ([tex]4(2)^2[/tex] - 4) / 2
= 2(4 - 1) = 2 x 3 = 6
Thus, the average rate of change = 6
c. The given function is f(x) = [tex]480(0.3)^x[/tex]
We have to find the average rate of change of this function from x = 1 to x = 5
The average rate of change = [tex]\frac{f(5)-f(1)}{5-1}[/tex]
= ([tex]480(0.3)^5 - 480(0.3)^1[/tex] ) / 4
= 480 (0.00243 - 0.3) /4
= 120 x -0.29757
Thus, the average rate of change = -35.7084
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The complete question is -
a. what is the average rate of change of the function f(x)= [tex]120(0.1)^x[/tex] from x = 0 to x = 2?
b. what is the average rate of change of the function f(x)= [tex]4(2)^x[/tex] from x = 0 to x = 2?
c. what is the average rate of change of the function f(x)= [tex]480(0.3)^x[/tex] from x = 1 to x = 5?
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