Answer:
The Exponential function is
[tex]y=4^x[/tex]
And the polynomial function is
[tex]y=7 x^2 +4 x -2[/tex]
And, we have to find the value of x for which, exponential function exceeds the polynomial function which can be written as
[tex]4^x> 7 x^2 +4 x -2[/tex]
1. When , x= -1
LHS
[tex]4^{-1}=\frac{1}{4}=0.25[/tex]
RHS
[tex]=7*(-1)^2 +4 *(-1)-2\\\\=7-4-2=1[/tex]
2. When , x=0
L HS
[tex]4^0=1[/tex]
RHS
[tex]7*0+4*0-2= -2[/tex]
3. When ,x= 0.5
L HS
[tex]4^{0.5}=2[/tex]
RHS
[tex]=7*0.25 +4*0.5 -2\\\\= 1.75+2-2\\\\=1.75[/tex]
4. When , x=2
LHS
[tex]4^{2}=16[/tex]
RHS
[tex]=7*4^2+4*4-2\\\\=112+16-2\\\\=126[/tex]
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.
