Question

PLZ HELP! Answer nicely, please don't just take my points :)

(05.03 MC)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^−x and y = 8^x+^4 intersect are the solutions of the equation 2^−x = 8^x+^4.

Part B: Make tables to find the solution to 2^−x = 8^x+^4. Take the integer values of x between −3 and 3.

Part C: How can you solve the equation 2^−x = 8^x+^4 graphically?

Answer 1

Step-by-step explanation:

Part A: The x-coordinate of the point where the graphs of the equations y = 2^−x and y = 8^(x+4) intersect is the solution of the equation 2^−x = 8^(x+4) because that value of x make the values of y the same. That is, for that value of x, the point (x, y) lies on the graph of both curves.

Part B: The attachment shows a table to find the solution to 2^−x = 8^(x+4). It has integer values of x between −3 and 3.

Part C: You solve the equation 2^−x = 8^x+^4 graphically by plotting the points found in part B, or by using a graphing utility. The solution is the point where the graph of y=2^-x intersects the graph of y=8^(x+4). That point is ...

(x, y) = (-3, 8)