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: Identify the formula

The formula for exponential decay is \(P = P_0(1 - r)^t\), where \(P_0\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time. Here, \(P_0=387\), \(r = 0.08\), and \(t = 8\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate \((0.92)^8\)

\((0.92)^8=0.92\times0.92\times0.92\times0.92\times0.92\times0.92\times0.92\times0.92\approx0.513212\)

Step4: Calculate \(P\)

\(P = 387\times0.513212\approx199.6\)

Answer:

\(199.6\)