Question

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.
5,000 = 25,000(0.043)t
B.
25,000 = 5,000(1.043)t
C.
5,000 = 25,000(0.957)t
D.
25,000 = 5,000(1.43)t

Answer 1

The correct option is: B.
`25000=5000(1.043)^t`

Step-by-step explanation

The general form of growth equation is:
`A=P(1+r)^t` , where A = final amount, P = initial amount, r = growth rate in decimal form and t = time duration

Here, the speed of the rocket at the beginning was 5,000 kilometers per hour and at the end will be 25,000 kilometers per hour. The speed increases at a rate of 4.3% per minute.

That means,
`A= 25000 , P= 5000, r= 4.3\% = 0.043`

Now plugging these values into the above equation, we will get......

`25000=5000(1+0.043)^t\\ \\ 25000=5000(1.043)^t`

So, the equation that could be used to determine the time for the speed of the rocket to reach 25,000 kilometers per hour will be:
`25000=5000(1.043)^t`