Respuesta :

absor201

Answer:

f(x) = 4(2/3)ˣ represents exponential decay.

Hence, option D is the correct function.

Step-by-step explanation:

The function of the form

[tex]y\:=\:a\left(1\:-\:r\right)^x\:\:[/tex]

where [tex]a > 0[/tex] and [tex]0 < r < 1[/tex]

is called the exponential decay function.

If we replace base 'b' by 1 - r, then we get the decay function of the form

y = abˣ

where 0 < b < 1

  • Please note that an exponential function cannot have a base of 0, 1, or a negative value.

Now, if we carefully observe, the function f(x) = 4(2/3)ˣ is the only option correct as

f(x) = 4(2/3)ˣ

here  0 < b < 1  and a > 0

Therefore, f(x) = 4(2/3)ˣ represents exponential decay.

Hence, option D is the correct function.

abidemiokin

The function that represents exponential decay is [tex]f(x)=4(\frac{2}{3} )^x[/tex] since 2/3 is less than 1.

Exponential functions

The standard expression for an exponential function is expressed as:

[tex]y=ab^x[/tex]

  • Note that the value of "b" determines whether an exponential equation is a growth or decay.
  • If b < 1, hence the exponential function is a decay
  • If b > 1, then the exponential function is growth.

From the given options, we can see that the function that represents exponential decay is [tex]f(x)=4(\frac{2}{3} )^x[/tex] since 2/3 is less than 1.

Learn more on exponential functions here: https://brainly.com/question/12940982

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