Without graphing determine whether the function represents exponential growth or exponential decay. Y=4(5/6)^x Y=12(17/10)^x Y=129(1.63)^x

Part A:

An exponential function is of the form [tex]y=a(b)^x[/tex], where b is a positive number not equal to 1.

The value of b determines whether tha function is an exponential growth or an exponential decay.

An exponential function is an exponential growth if b > 1 and an exponential decay if b < 1.

Given the function

[tex]y=4\left( \frac{5}{6} \right)^x \\ \\ \Rightarrow b= \frac{5}{6} \ \textless \ 1[/tex]

Therefore, the function [tex]y=4\left( \frac{5}{6} \right)^x[/tex] is an exponential decay.



Part B:

Given the function

[tex]y=12\left( \frac{17}{10} \right)^x \\ \\ \Rightarrow b= \frac{17}{10} \ \textgreater \ 1[/tex]

Therefore, the function [tex]y=12\left( \frac{17}{10} \right)^x[/tex] is an exponential growth.


Part C:

Given the function

[tex]y=129(1.63)^x \\ \\ \Rightarrow b= 1.63 \ \textgreater \ 1[/tex]

Therefore, the function [tex]y = 129(1.63)^x[/tex] is an exponential growth.