Question

The first stage of the Saturn 5 rocket that propelled astronauts to the moon burned about 8% of its remaining fuel every 15 seconds and carried about 600,000 gallons of fuel at liftoff. Estimate the amount of fuel remaining, to the nearest 10 thousand gallons, in the first stage 2 minutes after lift off.

Answer 1

590,000 gallons

Step-by-step explanation:

The rocket carried 600,000 gallons of fuel at liftoff.

It burned about 8% of its remaining fuel every 15 seconds.

This is an example of a reduction by a constant factor. We can model it using the depreciation function below:

`\begin{gathered} V(t)=V_o(1-r)^{(t)/(15)} \\ V(t)=600,000(1-0.08)^{(t)/(15)} \\ V(t)=600,000(0.92)^{(t)/(15)} \end{gathered}`

Note: t is in minutes.

So, the amount of fuel remaining in the first stage 2 minutes after liftoff will be:

`\begin{gathered} V(2)=600,000(0.92)^{(2)/(15)} \\ =593,366 \\ \approx590,000(to\text{ the nearest ten thousand gallons)} \end{gathered}`

In 2 minutes after liftoff, the amount of fuel remaining, to the nearest 10 thousand gallons is 590,000.