Find the points of intersection of the equations y = 2x + 2 and y = 2^x.

To solve the equations ( y = 2x + 2 ) and ( y = 2^x ), we can find their intersection points by setting them equal to each other:

1. Set the equations equal:

[

2x + 2 = 2^x

]

2. This equation is non-linear, so it may not be easy to solve algebraically. You can either graph both functions or test for values of ( x ).

Testing values:

– For ( x = 0 ):

[

y = 2(0) + 2 = 2

]

[

y = 2^0 = 1

]

Not an intersection.

– For ( x = 1 ):

[

y = 2(1) + 2 = 4

]

[

y = 2^1 = 2

]

Not an intersection.

– For ( x = 2 ):

[

y = 2(2) + 2 = 6

]

[

y = 2^2 = 4

]

Not an intersection.

– For ( x = 3 ):

[

y = 2(3) + 2 = 8

]

[

y = 2