If the first and second differences are not equal, find the ratios between the successive y-values.
y=3(2)^x
Practice makes perfect
To write an equation, we first need to determine the type of function that best models data. Then, we can use the general form of this type to write a function. Let's find the first differences. If they are not equal, we will find the second differences.
We see that neither the first differences nor the second differences are constant. Hence, the table represents neither a linear nor a quadratic function. Now, we will check if there is a constant ratio between the successive y-values.
We see that there is constant ratio of 2 between each consecutive terms. Therefore, an exponential function models the data.
y=a(b)^x
Here, a is the initial value and b is the constant multiplier. Then, a=3 and b=2
y=a(b)^x ⇔ y=3(2)^x
