Question

Graph the functions and approximate an x-value in which the exponential function exceeds the polynomial function. y = 4x y = 7x2 + 4x - 2

Answer 1

Answer:

The Exponential function is

$y=4^x$

And the polynomial function is

$y=7 x^2 +4 x -2$

And, we have to find the value of x for which, exponential function exceeds the polynomial function which can be written as

$4^x> 7 x^2 +4 x -2$

1. When , x= -1

LHS

$4^{-1}=\frac{1}{4}=0.25$

RHS

$=7*(-1)^2 +4 *(-1)-2\\\\=7-4-2=1$

2. When , x=0

L HS

 $4^0=1$

RHS

$7*0+4*0-2= -2$

3. When ,x= 0.5

L HS

 $4^{0.5}=2$

RHS

$=7*0.25 +4*0.5 -2\\\\= 1.75+2-2\\\\=1.75$

4. When , x=2

LHS

 $4^{2}=16$

RHS

$=7*4^2+4*4-2\\\\=112+16-2\\\\=126$

The Minimum value for which  exponential function exceeds the polynomial function is , x= 0.5

But,there is other value for which  exponential function exceeds the polynomial function is , x=2.