Observing the Functions:

Functions:

• $f\left(x\right)=4x+3f(x)\; =\; 4x\; +\; 3$ (Linear function)
• $g\left(x\right)={\left(\frac{5}{3}\right)}^{x}g(x)\; =\; \backslash left(\; \backslash frac\{5\}\{3\}\; \backslash right)^x$ (Exponential function)

Sentences to Complete:

1. Over the interval $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_$______, the average rate of change of $gg$ is greater than the average rate of change of $ff$.
2. As the value of $xx$ increases, the average rates of change of $ff$ and $gg$ ___________, respectively.
3. When the value of $xx$ is equal to 7, the value of $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_\backslash \_$_______________.
4. It can be further generalized that a quantity increasing exponentially will ___________ exceed a quantity increasing linearly.

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