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?

Question

___ rounds

Answer 1

To solve how many rounds it will take for the number of obstacles to reach 405 when starting with 15, and knowing that the number of obstacles triples each round, we can set up the following equation.

Let \( n \) be the number of rounds. We have:

\[ \text{Obstacles after } n \text{ rounds} = 15 \cdot 3^n \]

We want to find \( n \) when this equals 405:

\[ 15 \cdot 3^n = 405 \]

Dividing both sides by 15 gives:

\[ 3^n = \frac{405}{15} \]

Calculating the right side:

\[ \frac{405}{15} = 27 \]

Thus, we have:

\[ 3^n = 27 \]

We know that \( 27 \) can be expressed as \( 3^3 \), so we set the exponents equal to each other:

\[ n = 3 \]

Therefore, it will take \( 3 \) rounds for the number of obstacles to reach 405.

\[ \boxed{3} \]