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A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f (x) with entries 18, 6, 2, two-thirds.
What is the decay factor of the exponential function represented by the table?

One-third
Two-thirds
2
6

Answer :

joshmg42765

Answer:

A. 1/3

Step-by-step explanation:

6/18 = 0.3333333333333333333

so in fraction it is 1/3

The decay factor is [tex]\frac{2}{3}[/tex].

Exponential function:

  • The mathematical expression [tex]f(x)=exp[/tex] or [tex]ex[/tex] denotes the exponential function.
  • The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

Solution -

The exponential function's decay factor, as shown in the table, is [tex]\frac{2}{3}[/tex].

Modeling a fading exponential function involves:

[tex]A(t)=A(0)(1-r)^{t}[/tex]

In which:

[tex]A(0)[/tex] is the initial value.

[tex]r[/tex] is the decay rate, as a decimal.

Since [tex]y[/tex] reduces by a factor of [tex]3[/tex] when x decreases by [tex]1[/tex], the decay rate, or [tex]r[/tex], can be calculated as follows:

[tex]1-r=\frac{1}{3} \\r=1-\frac{1}{3} \\r=\frac{2}{3}[/tex]

Therefore, the decay factor is [tex]\frac{2}{3}[/tex].

Know more about exponential functions here:

https://brainly.com/question/2456547

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