Question

10 - Mr. Sandler's CarAdam Sandler's car tire has a slow puncture which is losing pressure according to this formula: Pt=3000.94t where t is the time in minutes and Pt represents the tire pressure in kPa (kilopascals).If the recommended lowest tire pressure to drive safely is 73 kPa how much time does Adam Sandler have left before it is unsafe? Show your work.

Answer 1

The function P is given by:

`P(t)=300(0.94)^t`

The required time t is given by:

`300(0.94)^t=73`

Divide both sides of the equation by 300:

`\begin{gathered} 0.94^t=(73)/(300) \\ t\ln(0.94)=\ln((73)/(300)) \\ t=(\ln((73)/(300)))/(\ln(0.94))\approx22.84\text{ min} \end{gathered}`

Therefore, the required time is approximately 22.84 min