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Which is a stretch of an exponential decay function?

Which Is A Stretch Of An Exponential Decay Function class=

Sagot :

Answer:

The correct option is C. The function [tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex] is a stretch of an exponential decay function.

Step-by-step explanation:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is the initial value and b is the growth factor.

If b<1, then it represents a decay function and if b>1, then it represents a growth function.

Let k be a stretch and compression factor.

[tex]g(x)=kf(x)[/tex]

If k<1, then it represents vertical compression and if k>1, then it represents vertical stretch.

In third function

[tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex]

[tex]k > 1[/tex]

[tex]b < 1[/tex]

Therefore the function [tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex] is a stretch of an exponential decay function.