Question

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

Answer 1

Writing an Exponential Function given the Table

Answer:

$y = 0.1(4)^x$

Step-by-step 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 $\frac{y_{n}}{y_{n -1}}$, where $y_n$ is $y$ when $x = n$.

Solving for the Common Ratio:

$r = \frac{y_{n}}{y_{n-1}} \\ r = \frac{y_2}{y_{2-1}} \\ r = \frac{y_2}{y_1} \\r = \frac{1.6}{0.4} \\ r = 4$

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 $y = 0.1(4)^x$