Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. f(x) = 5x + 4 h(x) = x2 + 8x + 24

x = -3
x = 3
x = 4
x = 5

The exponential function is 
The polynomial function is  

We want a value of x as such that , so

> 

We are provided with four possible value of x. By process of trial and error, we will narrow down two values of x when the statement is changing from false to true

first, we try  by substituting into  and 

and 
so > which is not the inequality wanted

We try  by substituting into  and 
and , 
so  >  as wanted

We know that any values of  greater than three will give  greater than , so we narrow down to two values that make the statement changes from false to true.

There is one value between -3 and three that makes  greater than . From here we use the method of trial and error. 

We can start with the mid value between -3 and three which is 0


is less than  which isn't the inequality we want so here we narrow down the value of x must be between 0 and 3

We can try mid-value between 0 and three which is 1.5


is still less than , so we now narrow down the value of x between 1.5 and 3

We try again using the mid-value between 1.5 and three which is 2.25


We still have  less than  so we can narrow down further the value of x between 2.25 and 3 (which is quite a short interval already)

We can keep trying by choosing a value of x says x=2.6


We have  greater then  

The narrowing down process continues where we now have the interval of x between 2.25 and 2.6. Keeping to one decimal place we can find the 
value of x=2.4 is the approximate value where  is greater than .

x=2.4