a) b) c) d)
1) Examining each function, let's test considering that the average rate of change is given by:
[tex]\Delta=\frac{f(b)-f(a)}{b-a}[/tex]
2) So let's plug the functions:
[tex]\begin{gathered} a)\text{ }\Delta=\frac{(100)+2\text{ -\lbrack(0)+2\rbrack}}{100-0}=\frac{102-2}{100}=\frac{100}{100}=1 \\ b)\text{ }g(x)=2^x\text{ }\Delta=\frac{2^{100}-2^0}{100-0}=\frac{1.26\times10^{30}}{100}=1.26\times10^{28} \\ c)\text{ }h(x)\text{ = }111x-23\text{ }\Delta=\frac{111(100)-23\text{ -\lbrack{}111(0)-23}}{100}=111 \\ d)\text{ }p(x)\text{ = }50,000\times3^x\Delta=\frac{50,000-3^{100}-\lbrack50,000-3^0}{100}=-5.15\times10^{45} \\ e)q(x)=87.5 \end{gathered}[/tex]
3) Since the average rate of change is a "measure of how much a function changes in the given interval" and considering that we have linear and exponential functions and the last one e) is not a function but an equation.
Then we can say that for the functions below the average rate of change is a good measure, not applying for the last one which, indeed is not a function.
a)
b)
c)
d)
