in general, how does the growth of y = 4^x compare to the growth of y = 4x?\nthe function y = 4^x is growing…

Explanation:

Step1: Analyze function types

$y = 4x$ is a linear function with a constant - slope of 4. Its rate of change is constant.

Step2: Analyze exponential function

$y = 4^{x}$ is an exponential function. The derivative of $y = 4^{x}$ is $y^\prime=4^{x}\ln(4)$ using the formula $\frac{d}{dx}(a^{x})=a^{x}\ln(a)$. As $x$ increases, the value of $4^{x}\ln(4)$ increases.

Step3: Compare growth rates

For small values of $x$, the linear function $y = 4x$ may be larger. But as $x$ gets larger, the exponential function $y = 4^{x}$ will grow much faster than the linear function $y = 4x$.

Answer:

The function $y = 4^{x}$ is growing faster than $y = 4x$.