Question

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

Answer 1

Writing an Exponential Function given the Table

Answer:

`y = 0.1(4)^x`

Explanation:

Given:

`&x &y \\ &0 &0.1 \\ &1 &0.4 \\ &2 &1.6 \\ &3 &6.4`

The most basic form to write an exponential function is
`y = ar^x`. Where
`a` is
`y` when
`x = 0`. We can see from the given Table of Values that at
`x = 0`,
`y = 0.1`. So,
`a = 0.1`. The
`r` is the common ratio and can be calculated by
`(y_(n))/(y_(n -1))\\`, where
`y_n` is
`y` when
`x = n`.

Solving for the Common Ratio:

`r = (y_(n))/(y_(n-1)) \\ r = (y_2)/(y_(2-1)) \\ r = (y_2)/(y_1) \\r = (1.6)/(0.4) \\ r = 4`

Now we know what
`r` and
`a` are. We can finally write the equation of the exponential function depicted by the table.

The equation is
`y = 0.1(4)^x`