Write an equation for the line that passes through the given points (2,3), (3,7)
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Answer:
Step-by-step explanation:
We will use 2 coordinates from the table along with the standard form for an exponential function to write the equation that models that data. The standard form for an exponential function is
where x and y are coordinates from the table, a is the initial value, and b is the growth/decay rate. I will use the first 2 coordinates from the table: (0, 3) and (1, 1.5)
Solving first for a:
. Sine anything in the world raised to a power of 0 is 1, we can determine that
a = 3. Using that value along with the x and y from the second coordinate I chose, I can then solve for b:
. Since b to the first is just b:
1.5 = 3b so
b = .5
Filling in our model:
Since the value for b is greater than 0 but less than 1 (in other words a fraction smaller than 1), this table represents a decay function.