Question

use the information to complete the following sentence.
the function ( f(t) = sqrt{t} + 300 ) is used to model the number of students in a training program where ( t ) represents days and ( f(t) ) represents the number of students.
it takes (\boxed{}) days for there to be 316 students in the program.

Explanation:

Step1: Set up the equation

We know that \( f(t)=\sqrt{t} + 30 \) and we want to find \( t \) when \( f(t) = 35 \) (assuming the number of students is 35, since the problem mentions 35 students, maybe a typo in the image but following the logic). So we set up the equation:
\( \sqrt{t}+30 = 35 \)

Step2: Solve for \( \sqrt{t} \)

Subtract 30 from both sides of the equation:
\( \sqrt{t}=35 - 30 \)
\( \sqrt{t}=5 \)

Step3: Solve for \( t \)

Square both sides of the equation to solve for \( t \):
\( t = 5^{2} \)
\( t = 25 \)

Answer:

25