Look at this table:
x y
–
1 0.99
0 2.97
1 8.91
2 26.73
3 80.19
Write a linear function
(y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
It seems that an exponential function would best model this data because the y-values are increasing rapidly as the x-values increase.
To find the exponential function, we can use the formula y = ab^x, where a is the initial value, b is the base, and x is the exponent.
Let's find the values of a and b.
x = 0, y = 2.97
2.97 = ab^0
2.97 = a
Now we have the value of a, which is 2.97.
x = 1, y = 8.91
8.91 = 2.97(b^1)
8.91 = 2.97b
b ≈ 2.997
Now we have the value of b, which is approximately 2.997.
Therefore, the exponential function that models the data is:
y = 2.97(2.997)^x