Q:

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the solutions of the equation 8^x = 2^x + 2. Part B: Make tables to find the solution to 8^x = 2^x + 2. Take the integer values of x between βˆ’3 and 3. Part C: How can you solve the equation 8^x = 2^x + 2 graphically? (Very confused, any help would be great!)

Accepted Solution

A:
Answer:Step-by-step explanation:Part A:We have two equations in the given question:y=8x and y=2x+2Then these two equations will intersect at a point where y is same fro both the equations:In equation y=8x we will exchange y with the other equation which is y=2x+2 then we would have Β 8x=2x+2..Part B:8x = 2x + 2. Take the integer values of x between βˆ’3 and 3x= -38(-3)=2(-3)+2-24=-6+2-24= -4It is falseNow plug x= -28(-2)=2(-2)+2-16 = -4+2-16 = -2This is falseNow plug x= -18(-1)=2(-1)+2-8 = -2+2-8=0It is falseNow plug x= 08(0)=2(0)+20=0+20=2It is falseNow plug x= 18(1)=2(1)+28=2+28=4FalseNow plug x= 28(2)=2(2)+216=4+216=6False Now plug x=38(3)=2(3)+224=6+224=8It is falseIt means there is no solution to 8x=2x+2 for the integers values of x between βˆ’3 and 3Part C:Plot the two given functions on a coordinate plane and identifying the point of intersection(values of the variables which satisfy both equations at a particular point) of the two graphs.The graph is attached. The point of intersection at x =0.333 and value of y = 2.667....