both of these functions grow as x gets larger and larger. which function eventually exceeds the…

both of these functions grow as x gets larger and larger. which function eventually exceeds the other?\n$f(x)=8x + 3.3$\n$g(x)=3.3^{x}-5$

both of these functions grow as x gets larger and larger. which function eventually exceeds the other?\n$f(x)=8x + 3.3$\n$g(x)=3.3^{x}-5$

Answer

Explanation:

Step1: Recall function - growth rates

Exponential functions (a^x) ((a> 1)) grow faster than linear functions (mx + b) as (x\to+\infty). The function (f(x)=8x + 3.3) is a linear function with slope (m = 8) and (y) - intercept (b = 3.3). The function (g(x)=3.3^x-5) is an exponential function with base (a = 3.3>1).

Step2: Analyze the long - term behavior

As (x) gets larger and larger, the exponential function (g(x)=3.3^x - 5) will eventually exceed the linear function (f(x)=8x + 3.3).

Answer:

The function (g(x)=3.3^x - 5) eventually exceeds the function (f(x)=8x + 3.3).