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Select the correct answer.In stage 2 of a rocket's takeoff, the speed of the rocket increases at a rate of 4.3% per minute. The speed of the rocket at the beginning of stage 2 was 5,000 kilometers per hour. Its speed at the end of Stage 2 will be 25,000 kilometers per hour.If t is the time, in minutes, from the beginning of stage 2, which equation could be used to determine how long it will take for the speed of the rocket to reach 25,000 kilometers per hour, assuming it increases at the same rate for all of stage 2? A. 25,000=5,000⁢(1.043)𝑡 B. 5,000=25,000⁢(0.043)𝑡 C. 25,000=5,000⁢(1.43)𝑡 D. 5,000=25,000⁢(0.957)𝑡

Question

Select the correct answer.In stage 2 of a rocket's takeoff, the speed of the rocket increases at a rate of 4.3% per minute. The speed of the rocket at the beginning of stage 2 was 5,000 kilometers per hour. Its speed at the end of Stage 2 will be 25,000 kilometers per hour.If t is the time, in minutes, from the beginning of stage 2, which equation could be used to determine how long it will take for the speed of the rocket to reach 25,000 kilometers per hour, assuming it increases at the same rate for all of stage 2? A. 25,000=5,000⁢(1.043)𝑡 B. 5,000=25,000⁢(0.043)𝑡 C. 25,000=5,000⁢(1.43)𝑡 D. 5,000=25,000⁢(0.957)𝑡

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Solution

To determine which equation could be used to find the time t t it takes for the rocket's speed to reach 25,000 kilometers per hour, we need to understand the relationship between the initial speed, the rate of increase, and the final speed.

Given:

  • Initial speed at the beginning of stage 2: 5,000 5,000 kilometers per hour
  • Final speed at the end of stage 2: 25,000 25,000 kilometers per hour
  • Rate of increase: 4.3% 4.3\% per minute

The speed of the rocket increases exponentially at a rate of 4.3% 4.3\% per minute. This can be represented by the formula for exponential growth:

Final Speed=Initial Speed×(1+Rate)t \text{Final Speed} = \text{Initial Speed} \times (1 + \text{Rate})^t

Where:

  • Final Speed=25,000\text{Final Speed} = 25,000 kilometers per hour
  • Initial Speed=5,000\text{Initial Speed} = 5,000 kilometers per hour
  • Rate=4.3%=0.043\text{Rate} = 4.3\% = 0.043
  • t t is the time in minutes

Substituting the given values into the formula, we get:

25,000=5,000×(1+0.043)t 25,000 = 5,000 \times (1 + 0.043)^t

Simplifying the expression inside the parentheses:

25,000=5,000×(1.043)t 25,000 = 5,000 \times (1.043)^t

This matches option A:

25,000=5,000×(1.043)t \boxed{25,000 = 5,000 \times (1.043)^t}

Therefore, the correct answer is:

A. 25,000=5,000×(1.043)t 25,000 = 5,000 \times (1.043)^t

This problem has been solved

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