Question

Which table shows exponential decay?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is A

Explanation for correct option(s):

What is exponential decay?

When the value of one variable of the function is decreased with increase in the number of other variable, then it is called the exponential decay function with constant exponential coefficient.

It can be given as,

$\frac{dN}{dt}=-\lambda N$

Here, $\lambda$ is the exponential coefficient.

The more the value of this exponential coefficient result in more exponential decay of the function.

Option : $A$

$\begin{array}{cc}x& y\\ 1& 16\\ 2& 8\\ 3& 4\\ 4& 2\end{array}$

the exponential coefficient for first and second row is,

$\lambda =\frac{16}{2}=2$

Similarly,

$$\begin{gathered} \lambda =\frac{8}{4}=2 \\ \lambda =\frac{4}{2}=2 \end{gathered}$$

Hence, as all the values of exponential coefficient is same, thus this shown the exponential decay.

Explanation for incorrect option(s)

Option : $B$

$\begin{array}{cc}x& y\\ 1& 16\\ 2& 12\\ 3& 8\\ 4& 4\end{array}$

the exponential coefficient for first and second row is,

$\lambda =\frac{16}{12}=\frac{4}{3}$

Similarly,

$$\begin{gathered} \lambda =\frac{12}{8}=\frac{3}{2} \\ \lambda =\frac{8}{4}=2 \end{gathered}$$

Option : $C$

$\begin{array}{cc}x& y\\ 1& 16\\ 2& 12\\ 3& 9\\ 4& 7\end{array}$

the exponential coefficient for first and second row is,

$\lambda =\frac{16}{12}=\frac{4}{3}$

Similarly,

$$\begin{gathered} \lambda =\frac{12}{9}=\frac{3}{4} \\ \lambda =\frac{9}{7} \end{gathered}$$

Option : $D$

$\begin{array}{cc}x& y\\ 1& 16\\ 2& 8\\ 3& 3\\ 4& 1\end{array}$

the exponential coefficient for first and second row is,

$\lambda =\frac{16}{8}=2$

Similarly,

$$\begin{gathered} \lambda =\frac{8}{3} \\ \lambda =\frac{3}{1}=3 \end{gathered}$$

For the option $B,C,andD$ the value of exponential coefficient is not same.

The data given in the table $A$ , the value of $y$ decreases with increase in the value of $x$ with constant exponential coefficient.

Thus the table $A$ shows the exponential decay.

Therefore, the correct answer is option $A$.