How do you write an exponential function whose graph passes through the points (0,-18) and (-2,-2)?

Question

9798 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-15T18:55:59

We can have

#g(x) = -18(3)^x#

An exponential function is given by # y = a(b^x)#.

Setting up a system of equations, we have:

#-18 = ab^0#
#-2 = ab^(-2)#

We can immediately see from the first equation that #a= -18# because #b^0 =1# .

#-2 = -18b^(-2)#

#-2 = -18/b^2#

#b^2 = 9#

#b = +- 3#

But #b >0#.

So the only plausible function is #y = -18(3)^x#. We confirm graphically:
enter image source here

Hopefully this helps!