A substance undergoes radioactive decay according to dN/dt = −λN. If N₀ is the initial amount at t=0, the amount N at time t is: A. N₀ e^(λt) B. N₀ e^(−λt) C. N₀ + e^(−λt) D. N₀ − λt Answer: B) N₀ e^(−λt) Explanation: dN/N = −λ dt. Integrating gives log N = −λt + c. At t=0, N=N₀, so c = log N₀. log(N/N₀) = −λt, which yields N = N₀ e^(−λt).

imo class 12 differential equations

A substance undergoes radioactive decay according to dN/dt = −λN. If N₀ is the initial amount at t=0, the amount N at time t is:

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A substance undergoes radioactive decay according to dN/dt = −λN. If N₀ is the initial amount at t=0, the amount N at time t is:

Answer: B) N₀ e^(−λt)

Explanation: dN/N = −λ dt. Integrating gives log N = −λt + c. At t=0, N=N₀, so c = log N₀. log(N/N₀) = −λt, which yields N = N₀ e^(−λt).