Question

If the domain for f(x)=30x+50 and g(x)=2•4 to the power of x were all real numbers without any restrictions, select all true statements

Answer 1

If the domain for f(x)=30x+50 and
`g(x)=2\cdot 4^x` were all real numbers without any restrictions, select the all the true statements

A. g(x) outputs would eventually exceed f(x) outputs.

C. An exponential function will always eventually exceed a linear function

D. The rate of change of g(x) is increasing and the rate of change of f(x) is constant.

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular relation or function is defined.

Generally speaking, an exponential function with a positive rate of change represents an exponential growth rate function.

This ultimately implies that, an exponential growth rate function will eventually exceed an increasing quadratic function because its rate of change increases while the rate of change of a linear function remains the same (constant).

Consequently, the output values of g(x) would eventually exceed the output values of f(x).

Complete Question:

If the domain for f(x)=30x+50 and
`g(x)=2\cdot 4^x` were all real numbers without any restrictions, select the all the true statements

g(x) outputs would eventually exceed f(x) outputs

The rate of change of f(x) is increasing and the rate of change of g(x) is constant

A linear function will always eventually exceed a exponential function

An exponential function will always eventually exceed a linear function

The rate of change of g(x) is increasing and the rate of change of f(x) is constant

f(x) outputs will always be greater than g(x) outputs