Look at this table:x y–10 –937–9 –758.97–8 –599.68–7 –459.13–6 –337.32Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.y=Submit
Question
Look at this table:x y–10 –937–9 –758.97–8 –599.68–7 –459.13–6 –337.32Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.y=Submit
Solution
The data provided seems to be decreasing at an increasing rate, which suggests that it could be modeled by an exponential function of the form y = a(b)^x.
To find the values of a and b, we can use two points from the data. Let's use the points (-10, -937) and (-9, -758.97).
First, we set up two equations using the form y = a(b)^x:
-937 = a(b)^-10 -758.97 = a(b)^-9
Dividing the second equation by the first one gives us:
-758.97/-937 = (a(b)^-9) / (a(b)^-10) 0.81 = b
Substituting b = 0.81 into the first equation gives us:
-937 = a(0.81)^-10 a = -937 / (0.81)^-10 a = -0.01
So, the function that models the data is y = -0.01(0.81)^x.
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