Respuesta :
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. [tex]N_0 = 240[/tex]
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, [tex]N(t) = N_o + 44t[/tex]
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, [tex]N(t) = N_o - 32t[/tex]
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,
[tex]N(t) = N_o + 20t\\N(t) = 240 + 20 t[/tex]
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
[tex]N(t) = N_o - 6t\\N(t) = 240 - 6 t[/tex]
e) Remained constant
[tex]N(t) = N_o\\N(t) = 240[/tex]
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
[tex]N(t) = N_o + 10t\\N(t) = 240 + 10 t[/tex]
