The average rate of change is ...
... (change in f(x))/(change in x)
... = (f(10) - f(2))/(10 - 2)
... = (10.24 - 0.04)/8 = 10.2/8 = 1.275
The average rate of change of f(x) from x=2 to x=10 is:
1.275
The average rate of change of a function f(x) from x=a to x=b is given by the formula:
[tex]Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}[/tex]
The function f(x) is given by:
[tex]f(x)=0.01\cdot 2^x[/tex]
We need to find the average rate of change of f(x) from x=2 to x=10
Hence, the average rate of change is calculated by:
[tex]Rate\ of\ change=\dfrac{f(10)-f(2)}{10-2}\\\\i.e.\\\\Rate\ of\ change=\dfrac{0.01\cdot 2^{10}-0.01\cdot 2^2}{8}\\\\Rate\ of\ change=\dfrac{0.01\times 2^2(2^8-1)}{8}\\\\i.e.\\\\Rate\ of\ change=\dfrac{0.01\times 255}{2}\\\\Rate\ of\ change=1.275[/tex]
Hence, the answer is: 1.275
