Question

the weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours. daryl plans to be gone for at least 6 hours, and he has a plant outside. if he wants the plant to remain in temperatures above -10°c, should daryl move his plant to a warmer location before leaving?
an inequality to model the problem is
the solution is

Explanation:

Step1: Define variables and model temperature change

Let \( t \) be the number of hours. The initial temperature is \( 20^\circ\text{C} \), and it drops \( 5^\circ\text{C} \) per hour, so the temperature after \( t \) hours is \( 20 - 5t \). We want the temperature to be above \( - 10^\circ\text{C} \), so the inequality is \( 20-5t > - 10 \).

Step2: Solve the inequality for \( t = 6 \) (since he is gone for at least 6 hours)

First, solve the inequality \( 20-5t > - 10 \) for \( t \):
Subtract 20 from both sides: \( - 5t> - 10 - 20 \)
Simplify: \( - 5t> - 30 \)
Divide both sides by - 5 (remember to reverse the inequality sign): \( t < 6 \)

But Daryl is gone for at least 6 hours (\( t\geq6 \)). When \( t = 6 \), the temperature is \( 20-5\times6=20 - 30=- 10^\circ\text{C} \), but we need the temperature above \( - 10^\circ\text{C} \). For \( t\geq6 \), \( 20 - 5t\leq - 10 \) (since when \( t = 6 \), it's equal, and for \( t>6 \), it's less than - 10).

Answer:

An inequality to model the problem is \( \boldsymbol{20 - 5t > - 10} \).

The solution shows that when \( t\geq6 \) (the time Daryl is gone), the temperature \( 20 - 5t\leq - 10 \), which is not above \( - 10^\circ\text{C} \). So Daryl should move his plant to a warmer location.