Question

The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10,000(1.1). The number ...

Answer 1

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The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10000.$(1.1)^{t}$. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t) = 450 + 40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.

Write a formula for D(t) in terms of S(t) and C(t).

Write a formula in terms of t.

Answer: D(t) = S(t) / C(t)

D(t) = $\frac{10000.(1.1^{t} )}{450+40t}$

Step-by-step explanation: First, it is asked to write D(t), which is the average number of students per classroom in terms of students, S(t) and classroom, C(t).

Average is the total number of students divided by the total number of classrooms. Therefore:

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

Second, to write in term of t, which is time in years, for the average number of students per classroom:

D(t) = $\frac{10000.(1.1)^{t} }{450+40t}$

In this formula it is clear that the average number of students per classroom is dependent of the growth factor of students each year represented by $1.1^{t}$ and the "growth factor" of classroom each year, represented by 40t.