Answer:
Part a) The y-intercept of the linear function is the point [tex](0,9)[/tex]
Part b) The y-intercept of the exponential function is the point [tex](0,1)[/tex]
Part c) One point of intersection
Part d) The x-coordinate of the solution is [tex]1[/tex]
Part e) The y-coordinate of the solution is [tex]7[/tex]
Step-by-step explanation:
we have
[tex]y=2(4^{x})-1[/tex] -------> equation A
[tex]y=-2x+9[/tex] ------> equation B
Part a) we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For [tex]x=0[/tex]
[tex]y=-2(0)+9=9[/tex]
The y-intercept is the point [tex](0,9)[/tex]
Part b) Find the y-intercept of the exponential function
For [tex]x=0[/tex]
[tex]y=2(4^{0})-1=1[/tex]
The y-intercept is the point [tex](0,1)[/tex]
Part c) The number of points of intersection
using a graphing tool
see the attached figure
One point of intersection
Part d) The x-coordinate of the solution
we know that
The solution of the system of equations is the intersection point both graphs
The intersection point is [tex](1,7)[/tex]
therefore
The x-coordinate of the solution is [tex]1[/tex]
Part e) The y-coordinate of the solution
we know that
The solution of the system of equations is the intersection point both graphs
The intersection point is [tex](1,7)[/tex]
therefore
The y-coordinate of the solution is [tex]7[/tex]
