Questions: Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is given by E(t)=3600-90 t.

Transcript text: Terry is skiing down a steep hill. Terry's elevation, $E(t)$, in feet after $t$ seconds is given by $E(t)=3600-90 t$.

Solution

Solution Steps

Step 1: Understand the Problem

We are given a function $ E(t) = 3600 - 90t $ that represents Terry's elevation in feet after $ t $ seconds. Our task is to analyze this function to understand Terry's elevation over time.

Step 2: Identify Key Features of the Function

The function $ E(t) = 3600 - 90t $ is a linear function, where:

The initial elevation (when $ t = 0 $) is 3600 feet.
The rate of change of elevation is $-90$ feet per second, indicating that Terry is descending the hill.

Step 3: Calculate Specific Values

Let's calculate Terry's elevation at specific times to understand how the elevation changes:

At $ t = 0 $ seconds: \[ E(0) = 3600 - 90 \times 0 = 3600 \text{ feet} \]
At $ t = 10 $ seconds: \[ E(10) = 3600 - 90 \times 10 = 3600 - 900 = 2700 \text{ feet} \]
At $ t = 20 $ seconds: \[ E(20) = 3600 - 90 \times 20 = 3600 - 1800 = 1800 \text{ feet} \]

Final Answer

The function $ E(t) = 3600 - 90t $ describes Terry's elevation over time, with an initial elevation of 3600 feet and a descent rate of 90 feet per second. Specific elevations at given times are: