Writing an Exponential Function given the Table
Answer:
[tex]y = 0.1(4)^x[/tex]
Step-by-step explanation:
Given:
[tex]&x &y \\ &0 &0.1 \\ &1 &0.4 \\ &2 &1.6 \\ &3 &6.4[/tex]
The most basic form to write an exponential function is [tex]y = ar^x[/tex]. Where [tex]a[/tex] is [tex]y[/tex] when [tex]x = 0[/tex]. We can see from the given Table of Values that at [tex]x = 0[/tex], [tex]y = 0.1[/tex]. So, [tex]a = 0.1[/tex]. The [tex]r[/tex] is the common ratio and can be calculated by [tex]\frac{y_{n}}{y_{n -1}}\\[/tex], where [tex]y_n[/tex] is [tex]y[/tex] when [tex]x = n[/tex].
Solving for the Common Ratio:
[tex]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[/tex]
Now we know what [tex]r[/tex] and [tex]a[/tex] are. We can finally write the equation of the exponential function depicted by the table.
The equation is [tex]y = 0.1(4)^x[/tex]
