The pressure P bars at time t (minutes) within a pressure vessel is given by P =

Question

The pressure P bars at time t (minutes) within a pressure vessel is given by P = 99(1 - e^-0.48t) (a) Find the initial value of the pressure Give your answer as a (whole) number only (omit the "P = ") in bars (b) Find the value of the pressure after 1.96 minutes. Give your answer as a number only (omit the "P = "), in bars, correct to AT LEAST TO THREE DECIMAL PLACES (c) Find the value of the pressure once it has settled after a long period of time Give your answer as a (whole) number only (omit the "P =") in bars

Explanation / Answer

P = 99 (1 - e-0.48t)

(a) When t = 0,

P = 99 (1 - e-0.48*0)

= 99 (1 - e0)

= 99 (1 - 1)

= 99 * 0

= 0

(b) When t = 1.96

P = 99 (1 - e-0.48*1.96)

= 99 (1 - e-0.9408)

= 99 (1 - 0.3903)

= 99 * 0.6097

= 60.359

(c) When t is very long, 0.48t is also "very long" and -0.48t is "very small"

e-0.48t ~= 0

=> P = 99 (1 - 0)

= 99

Thus P =

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