Question

the enrollment at a new school increases at a constant percent rate. after y years , the number of students enrolled is given by the expression 52 • 3 y/5

Answer 1

After y years the number of students is given as,

$52\cdot3^{\frac{y}{5}}$

The number of students when school has opened can be determined as,

$52\cdot3^{\frac{0}{5}}=52$

Thus, the number of students when the school has opend is 52.

The number of years after which the number of students triple can be determined as,

$\begin{gathered} 52\cdot3^{\frac{y}{5}}=52\times3 \\ 3^{\frac{y}{5}}=3 \\ \frac{y}{5}=1 \\ y=5 \end{gathered}$

Thus, required value of number of years is 5.

The factor by which the number of enrollment increases from one year to another can be determined as,

$\begin{gathered} \frac{52\cdot3^{\frac{y+1}{5}}}{52\cdot3^{\frac{y}{5}}} \\ =3^{\frac{1}{5}} \end{gathered}$

Thus, the above expression gives the requried value of factor.