Look at this table:
x y
0 3
1 9
2 27
3 81
4 243
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
Apologies for the mistake. Let's reassess the data.
Looking at the table, we can see that as x increases by 1, y is multiplied by 3. This suggests that the relationship between x and y is an exponential function.
To find the exponential function that models the data, we need to determine the values of a and b in the equation y = a(b)^x.
Let's start by analyzing the pattern of y-values: 3, 9, 27, 81, 243. Looking closely, we can see that each y-value is equal to 3 raised to the power of x. Therefore, the value of b is 3.
Now, let's check the starting value of y when x = 0. From the data, when x = 0, y = 3. Applying this to the equation, we have:
3 = a(3)^0
3 = a(1)
a = 3
Now we have the values for a and b, so the exponential function that models the data is:
y = 3(3)^x
From the given data, we notice that as x increases, y also increases. Additionally, the ratio between each y-value and its corresponding x-value is not constant, indicating that it is not a linear relationship. Therefore, we can conclude that the data is modeled by an exponential function.
To find the exponential function, we can look at the pattern of the data. Notice that y is equal to 3 raised to the power of x. Therefore, the exponential function that models the data is:
y = 3^x