Respuesta :
Answer:
[tex]f(x) = 4(\frac{2}{3})^{x}[/tex]
Step-by-step explanation:
The first function is given as, [tex]f(x) = \frac{1}{2}(\frac{3}{2})^{x}[/tex].
Now, the value of this function increases i.e. value of f(x) increases as the x-value increases because [tex]\frac{3}{2} > 1[/tex].
Now, the second function is given as, [tex]f(x) = \frac{1}{2}(- \frac{3}{2} )^{x}[/tex].
This function can not be considered as a continuous function because [tex]- \frac{3}{2} < 0[/tex].
Again, the third function is given as, [tex]f(x) = 4(- \frac{2}{3})^{x}[/tex].
This function can also not be considered as a continuous function because [tex]- \frac{2}{3} < 0[/tex].
Finally, the fourth function is given to be, [tex]f(x) = 4(\frac{2}{3})^{x}[/tex].
In this function, the value of f(x) continuously decreases as the value of x increases, because [tex]0 < \frac{2}{3} < 1[/tex].
Therefore, this function represents exponential decay. (Answer)
The function that represents exponential decay is [tex]f(x)=4(\frac{2}{3} )^x[/tex]
The standard exponential function is expressed as [tex]y=ab^x[/tex]
- The value of the variable x determines whether an exponential function is a growth or decay.
- If the decay constant is positive, the exponential function is a growth function
- If the decay constant is negative, the exponential function is a decay function
- Also, if b > 1, it is an exponential growth while if b < 1, it is decay.
Hence from the listed options, the function that represents exponential decay is [tex]f(x)=4(\frac{2}{3} )^x[/tex]
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