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

2

Explanation:

Answer 2

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)=(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.