How do a construct an exponential equation given (0, -1) and (2, -36)?

Dec 30, 2015

Start with the general equation for an exponential ...

$y = a {b}^{x}$

Explanation:

Now solve for the constants a and b by inserting the values for x,y

$\left(0 , - 1\right) : - 1 = a {b}^{0} = a$

So, now we know that $a = - 1$. Continue to solve for b ...

$\left(2 , - 36\right) : - 36 = \left(- 1\right) {b}^{2} \rightarrow {b}^{2} = 36 \rightarrow b = 6$

Finally, insert a and b ..

$y = \left(- 1\right) {6}^{x}$

hope that helped