Question

Find the equation of the exponential function represented by the table below:x y0 51 152 453 135y=

Answer 1

In order to find the exponential function, let's use the model:

$y=a\cdot b^x$

Then, to find the values of a and b, let's use the first two points of the table:

$\begin{gathered} x=0,y=5\colon \\ 5=a\cdot b^0\to a=5 \\ \\ x=1,y=15\colon \\ 15=5\cdot b^1 \\ b=\frac{15}{5}=3 \end{gathered}$

So our function is:

$y=5\cdot3^x$