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. $5,000 = 25,000(0.957)^t$
b. $25,000 = 5,000(1.43)^t$
c. $5,000 = 25,000(0.043)^t$
d. $25,000 = 5,000(1.043)^t$

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the growth rate per period, and $t$ is the number of periods.

Step2: Identify values

Here, the initial speed $P = 5000$ km/h, the final speed $A = 25000$ km/h, and the growth rate $r = 4.3\% = 0.043$. So $1 + r = 1 + 0.043 = 1.043$.

Step3: Substitute into formula

Substituting the values into the exponential growth formula, we get $25000 = 5000(1.043)^t$.

Answer:

D. $25,000 = 5,000(1.043)^t$