zach and his friends are doing a physics lab on air pressure. first they fill a balloon with air until it…

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

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

Answer

Explanation:

Step1: Identify the decay - formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 387$ kilopascals, $r=0.08$, and $t = 8$.

Step2: Substitute the values into the formula

$A=387\times(1 - 0.08)^8=387\times0.92^8$.

Step3: Calculate $0.92^8$

$0.92^8=0.51322288$.

Step4: Calculate the final pressure

$A = 387\times0.51322288\approx198.6$.

Answer:

$198.6$