A submarine enters the sea at an initial speed of 2 meters per minute. The submarine's speed triples every minute. What is the submarine's speed after 5 minutes?
now --- 2 m/min
after 1 min --- 6 m/min
after 2 min --- 18 m/min
after 3 min --- 54 m/min
after 4 min --- 162 m/min
after 5 min --- 486 m/min
To find the submarine's speed after 5 minutes, we can use the formula for exponential growth, which is given by:
\( s = a * r^n \)
Where:
- \( s \) is the final speed
- \( a \) is the initial speed
- \( r \) is the rate of growth (in this case, the speed multiplier)
- \( n \) is the number of minutes
In this problem, the initial speed is 2 meters per minute, and the rate of growth is that the speed triples every minute. This means that the speed multiplier (\( r \)) is 3.
To find the speed after 5 minutes, we substitute these values into the formula:
\( s = 2 * 3^5 \)
Now, let's calculate the result:
\( s = 2 * 3^5 \)
\( s = 2 * 243 \)
\( s = 486 \)
Therefore, the submarine's speed after 5 minutes is 486 meters per minute.