Write an exponential function in the form y = ab^x that goes through points (0,20) and (8,5120)

9514 1404 393

  y = 20·2^x

Step-by-step explanation:

Use the given points to write two equations, then solve for 'a' and 'b'.

  20 = a·b^0 = a

  5120 = a·b^8 = 20·b^8   ⇒   256 = b^8

  b = 256^(1/8) = 2

Your function is ...

  y = 20·2^x

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.