Given the equation [tex]\( W \approx -0.414t + 129.549 \)[/tex], where [tex]\( W \)[/tex] represents the water level in cups and [tex]\( t \)[/tex] represents the time in minutes, we need to find the time [tex]\( t \)[/tex] when the water level [tex]\( W \)[/tex] is less than or equal to 64 cups.
1. Set up the inequality:
We need to find [tex]\( t \)[/tex] such that [tex]\( W \leq 64 \)[/tex]:
[tex]\[
-0.414t + 129.549 \leq 64
\][/tex]
2. Isolate the variable [tex]\( t \)[/tex]:
Subtract 129.549 from both sides of the inequality:
[tex]\[
-0.414t \leq 64 - 129.549
\][/tex]
Simplify the right-hand side:
[tex]\[
-0.414t \leq -65.549
\][/tex]
3. Solve for [tex]\( t \)[/tex]:
Divide both sides by -0.414. Note that dividing by a negative number reverses the inequality:
[tex]\[
t \geq \frac{-65.549}{-0.414}
\][/tex]
Simplify the division:
[tex]\[
t \geq 158.33091787439616
\][/tex]
4. Determine the closest multiple choice option:
The closest answer among the options (150, 160, 170, 180) to 158.33091787439616 is 160.
Therefore, according to the given equation, the water level would be less than or equal to 64 cups after about 160 minutes.
