Question

The number of students, SSS, serviced by the school system in the town of Emor, ttt years from 200020002000 can be modeled by the function S(t)=10{,}000(1.1)^tS(t)=10,000(1.1)
t
S, left parenthesis, t, right parenthesis, equals, 10, comma, 000, left parenthesis, 1, point, 1, right parenthesis, start superscript, t, end superscript. The number of classrooms, CCC, in the town of Emor, ttt years from 200020002000 can be modeled by the function C(t)=450+40tC(t)=450+40tC, left parenthesis, t, right parenthesis, equals, 450, plus, 40, t.
Let DDD be the average number of students per classroom in Emor's school system ttt years from 200020002000.
Write a formula for D(t)D(t)D, left parenthesis, t, right parenthesis in terms of S(t)S(t)S, left parenthesis, t, right parenthesis and C(t)C(t)C, left parenthesis, t, right parenthesis.
D(t)=D(t)=D, left parenthesis, t, right parenthesis, equals
Write a formula for D(t)D(t)D, left parenthesis, t, right parenthesis in terms of ttt.
D(t)=D(t)=D, left parenthesis, t, right parenthesis, equals

Answer 1

Answer:

The formula of D (t) is $\frac{1000\cdot (1.1)^{t}}{45+4t}$.

Step-by-step explanation:

The expression representing the number of students serviced by the school system in the town of Emor, t years from 2000 is:

$S(t)=10,000\cdot (1.1)^{t}$

And the expression representing the number of classrooms in the town of Emor, t years from 2000 is:

$C(t)=450+40t$

The expression D (t) represents the average number of students per classroom in Emor's school system t years from 2000.

Then the average number of students per classroom can be computed by:

Average number of students/classroom = Number of students/Number of classrooms

                                                          $D(t)=\frac{S(t)}{C(t)}$

                                                                  $=\frac{10000\cdot (1.1)^{t}}{450+40t}\\\\=\frac{1000\cdot (1.1)^{t}}{45+4t}$

Thus,the formula of D (t) is $\frac{1000\cdot (1.1)^{t}}{45+4t}$.