Question

When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ) , representing the number of students attending this charter school t years after 2000, assuming that the student population:__________

Answer 1

Complete Question:

When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ) , representing the number of students attending this charter school t years after 2000, assuming that the student population:

a) Increased by 44 students per year

b) Decreased by 32 students per year

c) Increased by 40 students every 2 years

d) Decreased by 24 students every 4 years

e) Remained constant

f) Increased by 5 students every semester (twice in a year)

Answer:

a) N(t) = 240 + 44t

b) N(t) = 240 - 32t

c) N(t) = 240 + 20t

d) N(t) = 240 - 6t

e) N(t) = 240

f) N(t) = 240 + 10t

Step-by-step explanation:

The original population of the students in year 2000 is 240.

I.e. $N_0 = 240$

Let the number of years = t

a) If the population increased by 44 students every year, the population, after t years, would have increased by 44t

Therefore, $N(t) = N_o + 44t$

N(t) = 240 + 44t

b) If the population decreased by 32 students per year, the population, after t years, would have decreased by 32t

Therefore, $N(t) = N_o - 32t$

N(t) = 240 - 32t

c) If the population Increased by 40 students every 2 years and increase is uniform per year, the population will increase by 40/2 = 20 students in 1 year. So in t years, the population would increase by 20 t.

Therefore,

$N(t) = N_o + 20t\\N(t) = 240 + 20 t$

d) Decreased by 24 students every 4 years

In 1 year, it decreases by 24/4 = 6 students

In t years, it decreases by 6t students

$N(t) = N_o - 6t\\N(t) = 240 - 6 t$

e) Remained constant

$N(t) = N_o\\N(t) = 240$

f) If the population increases by 5 students twice in a year

In 1 year, it increases by 5*2 = 10 students

In t years, it increases by 10t students

$N(t) = N_o + 10t\\N(t) = 240 + 10 t$