Question

Which function represents exponential decay? f(x) = One-half(2)x f(x) = Three-fourths(Negative one-fifth)x f(x) = 3(Seven-halves)x f(x) = 2(Two-thirds)x

Answer 1

Answer:              $f(x)=2(\dfrac{2}{3})^x$

Step-by-step explanation:

We know that the exponential decay equation is given by :-

$y=Ab^x$

, where A = initial value.

b = Multiplicative growth rate  ( b <1 for decay)

x= time period.

Note : b ≠1 and b>0.

Let's check all the functions:

• $f(x)=\dfrac{1}{2}(2)^x$

, here b =2 >1 , so this function does not represent exponential decay.

• $f(x)=\dfrac{3}{4}(-\dfrac{1}{5})$

here b = $-\dfrac{1}{5}$  but b should be greater than 0 for exponential function, so this function does not represent exponential decay.

• $f(x)=3(\dfrac{7}{2})^x$

Here , $b=\frac{7}{2}>1$ , so this function does not represent exponential decay.

• $f(x)=2(\dfrac{2}{3})^x$

Here , $b=\dfrac{2}{3}<1$  , so this function represents exponential decay.

Hence, the correct answer is $f(x)=2(\dfrac{2}{3})^x$ .

Answer 2

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

We will see that the correct option is:

• f(x) = 2*(2/3)^x

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The form of the general exponential decay is:

f(x) = A*(r)^x

Where A is the initial value, x is the variable, and r is the rate at which it decreases, where r must be a number between 0 and 1.

The given options are:

• f(x) = (1/2)*2^x
• f(x) = (3/4)*(-1/5)^x
• f(x) = 3*(7/2)^x
• f(x) = 2*(2/3)^x

Because r must be between zero and one, the only option that meets that requirement is the last one, where r = 2/3.

Then the function that represents an exponential decay is the last one:

• f(x) = 2*(2/3)^x

If you want to learn more, you can read:

https://brainly.com/question/19599469