Question

1. Given the following table and graph, write the equation to representthe exponential function.уy43-1-4210-2-4-20х1-12-0.5

Answer 1

In order to find the equation of this exponential function, let's use this model for an exponential equation:

$y=a\cdot b^x$

Now, using some of the points given, we can find the values of the coefficients 'a' and 'b':

$\begin{gathered} x=0,y=-2 \\ -2=a\cdot b^0 \\ a=-2 \\ \\ x=1,y=-1 \\ -1=-2\cdot b^1 \\ b=\frac{-1}{-2}=0.5 \end{gathered}$

So our function is:

$y=-2\cdot0.5^x$