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) = 4.9^x - 5 g(x) = 6.3x^2 - 5

both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x) = 4.9^x - 5 g(x) = 6.3x^2 - 5

Answer

Explanation:

Step1: Recall growth - rate of functions

Exponential functions (a^x) ((a>1)) grow faster than polynomial functions (b x^n) ((b>0,n>0)) as (x\to+\infty). The function (f(x)=4.9^x - 5) is an exponential - type function with base (a = 4.9>1), and the function (g(x)=6.3x^2 - 5) is a polynomial function of degree (n = 2).

Step2: Determine the result

As (x) gets larger and larger, the exponential function (f(x)=4.9^x - 5) will eventually exceed the polynomial function (g(x)=6.3x^2 - 5).

Answer:

(f(x)=4.9^x - 5) eventually exceeds (g(x)=6.3x^2 - 5)