A remote weather station models the snow depth, in centimeters, on a mountain peak using the function below, where is the number of days after March 5. What does the value represent in this model?

Solution available with step-by-step explanation

SAT Linear Functions Question 129 | Free SAT Prep | Aniko

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Question 129·Hard·Linear Functions

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A remote weather station models the snow depth, in centimeters, on a mountain peak using the function $S$ below, where $t$ is the number of days after March 5.

S(t)=82.4-3.6\,(t-4)

What does the value $82.4$ represent in this model?

For questions asking what a specific number in a linear function represents, first identify the meaning of the variable (here, $t$ as days after a given date). Then see for which input that number appears as the function value—often when a parenthesis like $(t-4)$ is zero. Finally, convert that input back into the real-world context (such as a specific date or time) and match it to the choice that correctly describes the quantity (value vs. rate vs. total change).

Hints

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Connect $t$ to specific dates

Write down what dates $t=0,1,2,3,4$ represent, starting from March 5.

Focus on when the extra term vanishes

In $S(t)=82.4-3.6(t-4)$ , for what value of $t$ does the $(t-4)$ part become $0$ ? What is $S(t)$ equal to at that moment?

Turn that $t$ -value into a date

Once you know the $t$ -value where $S(t)$ equals $82.4$ , count that many days after March 5 to find the corresponding calendar date, then match it to the choices.

Desmos Guide

Enter the function

In Desmos, type S(t) = 82.4 - 3.6 (t - 4) to graph the snow depth model.

Evaluate the function at the key time

In a new line, type S(4) to see the snow depth when $t=4$ ; note that this output equals the constant $82.4$ in the equation.

Relate $t=4$ to the date

Translate $t=4$ into a calendar date by counting 4 days after March 5, then choose the option that describes the snow depth on that date.

Step-by-step Explanation

Translate what $t$ means into calendar dates

The problem says $t$ is the number of days after March 5.

$t=0$ : March 5
$t=1$ : one day after March 5 → March 6
$t=2$ : March 7
$t=3$ : March 8
$t=4$ : four days after March 5 → (we will use this soon).

See when the $82.4$ shows up in the formula

The model is

S(t) = 82.4 - 3.6(t-4).

Ask: for what value of $t$ does the $-3.6(t-4)$ part become $0$ ?

Set $t-4=0$ , which gives $t=4$ .
Then

S(4) = 82.4 - 3.6(4-4) = 82.4 - 3.6\cdot 0 = 82.4.

So $82.4$ is the snow depth at $t=4$ days after March 5.

Match $t=4$ to the correct date and interpret the value

From Step 1, $t=4$ is four days after March 5, which is March 9.

So $S(4)=82.4$ means the snow depth is $82.4$ centimeters on March 9.
Therefore, $82.4$ represents the snow depth on March 9.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

Hints

Desmos Guide

Step-by-step Explanation