Correct option D) Base of exponential function [tex]g(x) = 15(1.25)^x[/tex] is greater than 1 , this function will exceed linear function [tex]f(x) = 0.25x + 25[/tex] .
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:
This function is a linear function with an equation of straight line , having slope and y-intercept as :
[tex]m=0.25\\c=25[/tex]
Graph for this function is attached below .
This function is an exponential function in the form of [tex]g(x) = a(b)^x[/tex] , 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 [tex]g(x) = 15(1.25)^x[/tex] is much more vertical than linear function [tex]f(x) = 0.25x + 25[/tex] . Since , base of exponential function [tex]g(x) = 15(1.25)^x[/tex] is greater than 1 , this function will exceed linear function [tex]f(x) = 0.25x + 25[/tex] .Correct option D)
Answer:
B) The exponential function will always exceed the linear function.
Step-by-step explanation:
