Practice question · Select all that apply
The model solves dN/dt = kN. Select every TRUE statement.
Hints
- Substitute t = 0 into the solution to identify one of the constants.
- If the rate is k times N and N itself is changing, can the rate be constant?
Show the answer
- A. A negative k gives decay
- B. N_0 is the amount present at time zero
- C. The rate dN/dt is proportional to the current amount N
- E. A positive k gives growth
Why
The defining equation makes the rate PROPORTIONAL to the current amount, so as N grows the rate grows too, that is what distinguishes exponential growth from linear growth, where the rate would be constant. Setting t = 0 gives N = N_0, identifying the initial amount.
Practise Applications of Differentiation
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