Question

A weather station on the top of a mountain reports that the temperature is currently -10*C and has been falling at a constant rate of 3*C per hour. If it continues to fall at this rate, find each indicated temperature.

What will the temperature be in 5 hours?


What was the temperature 8 hours ago?


PLEASE HELP ME!!!!

Answer 1

The temperature in 5 hours will be -25°C.

The temperature 8 hours ago was 14°C.

Explanation:

To find the temperature, y, in degrees Celsius at any given number of hours, x, from the current time, we can create a linear equation in the form y = mx + b, where m is the rate of change and b is the current temperature.

Given the current temperature is -10°C, then b = -10.

Given the temperature falls at a constant rate of 3°C per hour, then m = -3.

Substitute the values of m and b into the formula:

`\boxed{y = -3x - 10}`

where:

• y is the temperature in °C.
• x is the number of hours.

To calculate the temperature in 5 hours time, substitute x = 5 into the equation:

`\begin{aligned}\implies y&=-3(5)-10\\&=-15-10\\&=-25^(\circ)\text{C}\end{aligned}`

Therefore, the temperature in 5 hours will be -25°C.

To calculate the temperature 8 hours ago, substitute x = -8 into the equation. The value of x is negative since we want to find the temperature 8 hours before the current time.

`\begin{aligned}\implies y&=-3(-8)-10\\&=24-10\\&=14^(\circ)\text{C}\end{aligned}`

Therefore, the temperature 8 hours ago was 14°C.