Digital SATMath: AlgebraMedium
A scientist is conducting an experiment where the temperature, T, in degrees Celsius, inside a chamber is controlled by the equation T = |5t - 30| + 15, where t is the time in minutes. What is the minimum temperature reached in the chamber?
- A30°C
- B45°C
- C0°C
- D15°C
Show answer & explanationAnswer & explanation
Correct answer: D. 15°C
The absolute value function |5t - 30| will always be greater than or equal to 0. The minimum value of an absolute value expression is 0. Therefore, the minimum temperature occurs when |5t - 30| = 0, which means T = 0 + 15 = 15°C.
Why the other options are wrong
- A. This is the value that makes the absolute value term zero (5t-30=0 -> t=6), but not the minimum temperature itself.
- B. This value is higher than the minimum and likely results from incorrect calculation or interpretation.
- C. This would be the minimum if the constant term was 0, but it's 15.
Minimum of Absolute Value Function
The minimum value of an absolute value function of the form y = a|x - h| + k is k, and it occurs when x = h, making the absolute value term zero.
- The absolute value expression |X| is always ≥ 0.
- Its minimum value is 0.
- The minimum of y = |X| + k is k.
Memory trick: Absolute Min: The 'k' is the lowest, when the inside is zero!