Question

Find the equation of the exponential function represented by the table below:
т
y
0
4
12
36
108

Answer 1

We have a table that represents an exponential function.

We can express an exponential function as:

$y=a\cdot b^x$

We can use the values of the table to calculate the parameters "a" and "b".

For example we can use the value of y when x = 0 to calculate "a":

$\begin{gathered} y(0)=4 \\ a\cdot b^0=4 \\ a\cdot1=4 \\ a=4 \end{gathered}$

We then can use two consecutive values to find the parameter "b":

$\begin{gathered} \frac{y(2)}{y(1)}=\frac{a\cdot b^2}{a\cdot b^1}=b^{2-1}=b \\ \Rightarrow b=\frac{y(2)}{y(1)}=\frac{36}{12}=3 \end{gathered}$

Then, we can express the exponential function as:

$y=4\cdot3^x$

Answer: y = 4*3^x