Answer: 23.22
Step-by-step explanation:
Given function: [tex]f(x)=0.01(2)^x[/tex]
At x=7
[tex]f(7)=0.01(2)^7=1.28[/tex]
At x=14
[tex]f(14)=0.01(2)^{14}=163.84[/tex]
We know that the rate of change from [tex]x_1[/tex] to [tex]x_2[/tex] of function is given by
[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Therefore, The rate of change of given function from x=7 to x=14
[tex]=\frac{f(14)-f(7)}{14-7}\\\\=\frac{163.84-1.28}{14-7}\\\\=\frac{162.56}{7}\\\\=23.22[/tex]
Therefore, the average rate of change from x = 7 to x = 14 for the given function is 23.22
