To start, the first thing you need to do is to find the slope of your x and y values, or in other words, your rate of change. To do this, use the slope intercept formula or (y2-y1)/(x2-x1) and you can use any two pairs of x and y values.
Using the x and y values of (2, 96) and (3, 76.80), plug the values into the slope intercept formula. This would look like this: (76.80-96)/(3-2)
When you simplify, you should get -19.2/1 or simply -19.2 as your slope.
Then, using the linear equation y=mx+b, plug in a coordinate point into the x and y variables and plug your slope into the m value in order to solve for the value of your y-intercept, or b. This would look like this: 96=-19.2(2)+b
When you simplify, you will get 96=-38.4+b and when you solve for b, you get that b=134.4
Now that you have your slope and your y-intercept, you can conclude that the equation to this input/output chart would be y=-19.2x+134.4
It would help if you would post the complete question not just a few points in a table. Without all the information provided in the question ( initial value??); I can not be certain of the solution. Looking at the table, you can tell the rate is not constant, it changes between points. The data best fits an exponential decay graph. When plotted in excel it gives the equation:
with a perfect R² = 1 This equation shows that whatever this data represents started at 150 and exponentially decayed/decreased at a rate of -0.223
