Question

Write the exponential function for each table of values. Remember the function y = a(b)*

Answer 1

Answer:

Step-by-step explanation:

This is really simple once you get the hang of it. Promise. Remember this:

IF YOU HAVE THE OPPORTUNITY TO CHOOSE A POINT FROM THE TABLE WHERE X = 0, THEN DO IT!

This gives you the a value in your equation and you don't have to solve for it. I'll show you how this looks in the first table of values and then we won't have to do it going forward.

I'm using the coordinates (0, 1) and (1, .5) from the first table. Filling in the equation with the first set of coordinates:

$1=a(b)^0$ and since anything to the 0 power is 1, we know a = 1 (this happens every time we have a coordinate in an exponential table where the x value is 0. a always equals whatever y is!)

Now that we know a = 1, we use that along with the next coordinate pair and solve for b:

$.5=1(b)^1$ which simplifies to

.5 = b and the equation is

$y=1(.5)^x$

For the next table use the coordinate (0, 50) and 1, 25). From the above explanation, I know that a = 50 (because x = 0). Use that along with the next coordinate pair to solve for b:

$25=50(b)^1$ which simplifies to

b = .5 and the equation is

$y=50(.5)^x$

Lastly, use the points (0, 192) and (1, 768) and we know that a = 192; and it follows that

$768=192(b)^1$ so

b = 4 and the equation is

$y=192(4)^x$

The first 2 of these are exponential decay because the number inside the parenthesis is less than 1 but greater than 0; the last one is exponential growth since the number inside the parenthesis is greater than 1. That's how you can tell.