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