Question

carmen uses the function $f(t) = \sqrt{t + 100}$ to model the number of students in her after - school program. the variable $t$ represents days and $f(t)$ represents the number of students. how many days does it take for there to be 15 students in her program?\
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a. 115 days\
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b. 125 days\
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c. 225 days\
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d. 325 days

Explanation:

Step1: Set up the equation

We know that \( f(t)=\sqrt{t + 100} \) and we want to find \( t \) when \( f(t)=15 \). So we set up the equation \( 15=\sqrt{t + 100} \).

Step2: Square both sides

To eliminate the square root, we square both sides of the equation. \((15)^2=(\sqrt{t + 100})^2\), which simplifies to \( 225=t + 100 \).

Step3: Solve for t

Subtract 100 from both sides of the equation: \( t=225 - 100 \), so \( t = 125 \).

Answer:

B. 125 days