Question

problems 4 - 6: a weather station on top of a mountain reports that the temperature is currently 0°c and has been decreasing at a constant rate of 3 degrees per hour.

1. what will the temperature be in 5 hours?
2. what was the temperature 1 hour ago?
3. what was the temperature 3 hours ago?

Explanation:

Step1: Determine the formula for temperature change

The current temperature is $T_0 = 0^{\circ}C$, and the rate of change is $r=- 3^{\circ}C$ per hour (negative because it is decreasing). The formula for temperature $T$ after $t$ hours is $T = T_0+rt$.

Step2: Solve for question 4

For $t = 5$ hours, substitute into the formula: $T=0+( - 3)\times5$.
$T=-15^{\circ}C$

Step3: Solve for question 5

For $t=-1$ hour (1 hour ago), substitute into the formula: $T = 0+( - 3)\times(-1)$.
$T = 3^{\circ}C$

Step4: Solve for question 6

For $t=-3$ hours (3 hours ago), substitute into the formula: $T=0+( - 3)\times(-3)$.
$T = 9^{\circ}C$

Answer:

1. $-15^{\circ}C$
2. $3^{\circ}C$
3. $9^{\circ}C$