Question

1. model with math nocturnal mouse lemurs enter a state known as torpor each day to conserve energy. under certain conditions, their body temperatures drop to within 3° of 30°c. write a model and determine the range of temperatures a mouse lemur might experience.

Explanation:

Step1: Define the problem

We know the normal body temperature is around \(30^{\circ}C\) and the temperature drops within \(3^{\circ}\) of this value. We need to find the range of temperatures.

Step2: Set up the inequality

Let \(T\) be the body temperature of the mouse lemur. The temperature drops within \(3^{\circ}\) of \(30^{\circ}C\), so we can write the absolute - value inequality \(|T - 30|\leq3\).

Step3: Solve the absolute - value inequality

We know that if \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\). Applying this to \(|T - 30|\leq3\), we get:
\(- 3\leq T - 30\leq3\)

Step4: Solve for \(T\)

First, add 30 to all parts of the compound inequality:
For the left - hand side: \(-3 + 30\leq T-30 + 30\), which simplifies to \(27\leq T\)
For the right - hand side: \(T-30 + 30\leq3 + 30\), which simplifies to \(T\leq33\)

Answer:

The range of temperatures a mouse lemur might experience is \(27^{\circ}C\leq T\leq33^{\circ}C\)