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