Question

zach and his friends are doing a physics lab on air pressure. first they fill a balloon with air until it reaches a pressure of 387 kilopascals. then they prick the balloon and measure its pressure over time. according to their measurements, the balloon appears to be losing pressure at a rate of 8% every hour. if this trend continues, what will the pressure be in 8 hours? if necessary, round your answer to the nearest tenth. kilopascals

Explanation:

Step1: Define decay formula

This is exponential decay, use $P(t) = P_0(1-r)^t$, where $P_0=387$, $r=0.08$, $t=8$.

Step2: Calculate remaining factor

$1-r = 1-0.08 = 0.92$

Step3: Compute $0.92^8$

$0.92^8 \approx 0.5132$

Step4: Find final pressure

$P(8) = 387 \times 0.5132$

Answer:

198.6 kilopascals