Question

At noon on Monday, the air pressure of a tire is 32 pounds per square inch (psi). The tire loses 8% of its air every day. The tire pressure monitoring system (TPMS) will alert the driver when the tire pressure is less than or equal to 24 psi. On what day of the week will the TPMS alert the driver? Use the trace feature of a graphing calculator to help find the answer.

(a) Monday
(b) Tuesday
(c) Wednesday
(d) Thursday

Answer 1

The TPMS will alert the driver on Thursday.

Step-by-step explanation:

To find the day of the week when the TPMS will alert the driver, we need to determine how many days it takes for the tire pressure to reach or go below 24 psi. The tire loses 8% of its air every day, so we can set up an equation:

32 - 0.08(32) = 24

Solving for the number of days, we get:

0.92x = 24/32

By using a trace feature on a graphing calculator, we can find that x is approximately 3.22. This means that it will take about 3.22 days for the tire pressure to drop to or below 24 psi. Since we start at noon on Monday, the TPMS will alert the driver on Thursday.