Respuesta :

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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.
abidemiokin

Since 5/6 is less than 1, hence the exponential equation [tex]y=4(\frac{5}{6} )^x[/tex] is an exponential decay

Since 1.7 is greater than 1, hence the exponential equation [tex]y=12(\frac{17}{10})^x[/tex] is an

exponential growth

Since 1.63 is greater than 1, hence the exponential equation [tex]y =129(1.63)^x[/tex] is an exponential growth

The standard form of an exponential equation is [tex]ab^x[/tex]

The value of "b" in the expression determines whether the exponential equation given is s decay or an exponential growth

For the exponential equation [tex]y=4(\frac{5}{6} )^x[/tex]

Compared with the standard expression, we will see that b = 5/6

Since 5/6 is less than 1, hence the exponential equation [tex]y=4(\frac{5}{6} )^x[/tex] is an exponential decay

Similarly for the exponential equation [tex]y=12(\frac{17}{10} )^x =12(1.7)^x[/tex]

Compared with the standard expression, we will see that b = 1.7

Since 1.7 is greater than 1, hence the exponential equation [tex]y=12(\frac{17}{10})^x[/tex] is an

exponential growth

Also,  for the exponential equation [tex]y =129(1.63)^x[/tex]

Compared with the standard expression, we will see that b = 1.63

Since 1.63 is greater than 1, hence the exponential equation [tex]y =129(1.63)^x[/tex] is an exponential growth

Learn more here: https://brainly.com/question/12626186

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