Question

As x approaches ∞, which statement is correct?

A) The linear function will eventually exceed the exponential function.
B) The exponential function will eventually exceed the linear function.
C) The exponential function will only exceed the linear function if it has a greater growth factor.
D) The linear function will only exceed the exponential function if it has a greater common difference.

Answer 1

b

Explanation:

The exponential function will always exceed the linear function.A quantity increasing exponentially eventually exceeds a quantity increasing linearly.

Answer 2

B

Explanation:

This is very simple if we understand a point of linear and exponential functions.

First of all, a linear growing function increases.

An exponential growing function increases as well.

But, linear function, no matter what the slope is, grows at a CONSTANT RATE. But,

Exponential function grows at a COMPOUND RATE.

So, if there are 2 functions, linear and exponential, the exponential will always exceed the linear, AT SOME POINT EVENTUALLY because of the growth factor (no matter growth factor of linear and exponential -- whatever they are).

So,

B is the correct answer.

Growth factor of each (both) doesn't matter. Exponential will always win!