When a new charter school opened in 2010, there were 850 students enrolled. Using function notation, write a formula representing the number, N, of students attending this charter school t years after 2010, assuming that the student population:
a) Increases by 9% per year

b) Decreases by 64 students per year

c) Remains constant (does not change)

d) Increases by 42 students per year

e) Decreases by 6% per year

To represent the number of students \( N(t) \) attending the charter school \( t \) years after 2010, we'll use function notation and create formulas based on each scenario provided.

Given:
- Initial enrollment in 2010: \( N(0) = 850 \)

### a) Population increases by 9% per year
If the student population increases by 9% per year, the function will be an exponential growth model:

\[
N(t) = 850 \times (1.09)^t
\]

### b) Population decreases by 64 students per year
If the student population decreases by 64 students per year, the function will be a linear model with a negative slope:

\[
N(t) = 850 - 64t
\]

### c) Population remains constant
If the student population remains constant, the function will be a constant function:

\[
N(t) = 850
\]

### d) Population increases by 42 students per year
If the student population increases by 42 students per year, the function will be a linear model with a positive slope:

\[
N(t) = 850 + 42t
\]

### e) Population decreases by 6% per year
If the student population decreases by 6% per year, the function will be an exponential decay model:

\[
N(t) = 850 \times (0.94)^t
\]

These formulas represent the number of students \( N(t) \) attending the charter school \( t \) years after 2010 under the different scenarios.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the formulas change if the initial number of students was different?
2. What would happen to the student population after 10 years for each scenario?
3. How do exponential growth and decay models differ in behavior over time?
4. How would you calculate the exact number of students after 5 years for each scenario?
5. Can you derive a general formula for any percentage increase or decrease per year?

**Tip:** For exponential functions, small changes in the rate of increase or decrease can have significant long-term effects.

Explore how the student population at a charter school changes over time based on different growth and decline scenarios. Includes formulas for exponential growth, linear decrease, constant population, linear increase, and exponential decay starting with an initial enrollment of 850 students in 2010.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation