Question

1. a rocket is being accelerated such that its speed triples every eight minutes in flight. if the speed was 6 meters per second when the acceleration began, what is its speed after 20 minutes of acceleration? (1) 85.7 meters per second (2) 88.2 meters per second (3) 93.5 meters per second (4) 101.8 meters per second

Explanation:

Step1: Calculate the number of 8 - minute intervals in 20 minutes

The number of 8 - minute intervals \(n=\frac{20}{8}=2.5\)

Step2: Use the formula for exponential growth \(y = a\times b^{n}\)

Here, \(a = 6\) (initial speed), \(b = 3\) (triples every interval)
\(y=6\times3^{2.5}\)
We know that \(3^{2.5}=3^{2}\times3^{0.5}=9\times\sqrt{3}\approx9\times1.732 = 15.588\)
\(y=6\times15.588 = 93.528\approx93.5\)

Answer:

(3) 93.5 meters per second