Question

Consider the functions:

Answer 1

Answer:

B) The exponential function will always exceed the linear function.

Step-by-step explanation:

Answer 2

Correct option D) Base of exponential function $g(x) = 15(1.25)^x$  is greater than 1 , this function will exceed linear function  $f(x) = 0.25x + 25$ .

Step-by-step explanation:

Here we have , f(x) = 0.25x + 25 and g(x) = 15(1.25)x . We need to tell As x approaches ∞, which function exceeds whom! Let's find out:

• f(x) = 0.25x + 25

This function is a linear function with an equation of straight line , having slope and y-intercept as :

$m=0.25\\c=25$

Graph for this function is attached below .

• g(x) = 15(1.25)^x

This function is an exponential function in the form of $g(x) = a(b)^x$ , where b>1 i.e. for rise in value of x there is exponential increase in value of y or , function .Basically Base of this exponential is greater than 1 , which makes it an increasing function ! Graph for this function is attached below .

Now , Comparing both graphs we see that as x approaches ∞ graph of exponential function $g(x) = 15(1.25)^x$ is much more vertical than linear function $f(x) = 0.25x + 25$ . Since , base of exponential function $g(x) = 15(1.25)^x$  is greater than 1 , this function will exceed linear function  $f(x) = 0.25x + 25$ .Correct option D)