- #1

i_m_mimi

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## Homework Statement

[10] The air pressure in an automobile's spare tire was initially 3000 millibar.

Unfortunately, the tire had a slow leak. After 10 days the pressure in the tire had declined to 2800 millibar. If P(t) is the air pressure in the tire at time t,then P(t) satises the dierential equation

dP/dt = −k(P(t)−A);

where k is a constant and A is the atmospheric pressure. For simplicity, take

atmospheric pressure to be 1000 millibar. When will the pressure in the tire be

2500 millibar?

answer:

10*[ln(4/3)]/[ln(10/9)]

## Homework Equations

## The Attempt at a Solution

P(t) = Ce^-kt

0 = 3000e^-k(0)

2800 = 3000 e^-k(10days)

k = -[ln 28/30]/10

2500 = 3000 e^[ln 28/30]t/10

t = 10 [ln 25/30]/[ln 28/30] wrong answer

dP/dt = 0.1 ln(28/30) (P(t) - 1000)

I can't figure out what is the function P(t) = ? or where to put in variable t, time. And where does the dP/dt equation come in? this is a complicated exam question worth 10 marks with 20 minutes allocated to it.

thank you