Question

Which of the following equations describe or result in exponential decay of a quantity n. τ,t1/2 and n0 are positive constants. Check all that apply.

(A) dn/dt=(n0−n)/τ
(B) dn/dt=−nτ
(C) n(t)=n0e^(−t/τ)
(D) n(t)=(n0)(2^(−t/t1/2))
(E) dn/dt=+nτ

Answer 1

(B) dn/dt=−nτ

(C) n(t)=n0e^(−t/τ)

(D) n(t)=(n0)(2^(−t/t1/2))

Explanation:

The formula for exponential decay is:

`\text{Final amount}=\text{Initial amount}* e^(-k* t)`

(A) Since the differentiate indicate the decay. Also, here we get positive value of differentiation. Thus, it does not show the exponential decay.

(B) Since the differentiate indicate the decay. Also, here we get negative value of differentiation. Thus, it show the exponential decay.

(C) Here Since it is similar to formula of exponential function also base is greater than 1(i.e. e) and power is less than 0(i.e. negative). It is exponential decay.

(D) Here Since it is similar to formula of exponential function also base is greater than 1(i.e. 2) and power is less than 0(i.e. negative). It is exponential decay.

(E) Since the differentiate indicate the decay. Also, here we get positive value of differentiation. Thus, it does not show the exponential decay.