Question

Find the equation of the exponential function represented by the table below: above^^^^

Answer 1

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

`y=a(b)^x` 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:

`3=a(b)^0`. 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:

`1.5=3(b)^1`. Since b to the first is just b:

1.5 = 3b so

b = .5

Filling in our model:

`y=3((1)/(2))^x`

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.