How do you write a rule for this exponential growth function if one point is at (-1,4) and the other is (0,3)?

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Answer 1 · 2017-07-08T01:10:41

Exponential growth can be written in many mathematically equivalent forms, #y = Cr^x, y = Ce^(lambdax), y = C(1+r)^x#, and so on.

I will use the following:

#y = Cr^x#

The point #(0,3)# allows us to find the value of C:

#3 = Cr^0#

Any number to the 0 power is 1:

#C = 3#

The point #(-1,4)# allows us to find the value of r:

#4 = 3r^-1#

#4/3=r^-1#

#r = 3/4#

#y = 3(3/4)^x#

Here is a graph:

graph{3(3/4)^x [-11.25, 11.25, -5.625, 5.625]}