Mandy is playing a game on her phone where the number of obstacles she has to avoid triples each round. If she is currently on a round with 15 obstacles, in how many rounds will there be 405 obstacles to navigate? obstacles

To determine how many rounds it will take for the number of obstacles to increase from 15 to 405 when the number triples each round, we can set up the following equation: \[ \text{Number of Obstacles} = 15 \times 3^n \] Where: - \( n \) is the number of rounds. - The initial number of obstacles is 15. - Each round, the obstacles triple, hence the \( 3^n \) term. We want to find \( n \) when the number of obstacles is 405: \[ 15 \times 3^n = 405 \] 1. **Divide both sides by 15:** \[ 3^n = \frac{405}{15} \] \[ 3^n = 27 \] 2. **Express 27 as a power of 3:** \[ 27 = 3^3 \] 3. **Set the exponents equal:** \[ n = 3 \] **Answer:** It will take **3 rounds** for the number of obstacles to reach 405.