Differential equation — Exponential growth equation

Step by step

1. Set up the solution: separate or integrate the differential equation, include the constant, then use the initial condition..
2. Simplify the previous line carefully, keeping exact values where possible., hence .
3. Finish the calculation, then check that the result meets the question’s conditions. gives .
4. State the final answer clearly in the form the question requested.Final answer:

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Differentiating gives and the initial value is .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.