both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x)…

both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x) = 8^x - 3 g(x) = 10x

both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x) = 8^x - 3 g(x) = 10x

Answer

Explanation:

Step1: Analyze growth - rate of exponential and linear functions

Exponential functions (y = a^{x}) ((a>1)) grow faster than linear functions (y = bx + c) ((b>0)) as (x\to+\infty). Here, (f(x)=8^{x - 3}=\frac{8^{x}}{8^{3}}=\frac{8^{x}}{512}) is an exponential function with base (a = 8>1), and (g(x)=10x) is a linear function.

Step2: Consider the long - term behavior

As (x) gets larger and larger, the exponential function (f(x)) will eventually exceed the linear function (g(x)).

Answer:

(f(x))