Question

Write an inequality that represents `t`, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning

Answer 1

Question:

At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.

Write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning.

Answer:

`t > 4.5`

Explanation:

Given

Let T = temperature and t = hours past midnight

So, we have:

`(t_1,T_1) = (0,5)` --- at midnight

`m = -2` --- rate (it is negative because the temperature drops)

Required

Determine the inequality when the temperature is colder than -4 degrees

First, we calculate the hours when the temperature at -4 degrees

This is represented as:

`(t_2,T_2) = (t,-4)`

`(t_1,x_1) = (0,5)`

Using the slope formula, we have:

`m = (T_2 -T_1)/(t_2 - t_1)`

`-2 = (-4-5)/(t -0)`

`-2 = (-9)/(t)`

Solve for t

`t = (-9)/(-2)`

`t = 4.5`

This implies that: at 4.5 hours, the temperature is at -4 degrees Celsius.

So, the inequality is:

`t > 4.5`