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6. A private school opened in 2005 with an initial enrollment of 85 students. The enrollment has increased by an average of 18 students each year since the school opened. A nearby public school had an enrollment of 95 in 2005, and its enrollment has increased by an average of 15 students per year.

a. Let t = time in years, with t = 0 representing the year 2005. Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school. Create the two functions to represent the situation.

f(t) = 18t + 85
g(t) = 15t + 95 < correct?

b. Graph the system of equations to determine thepoint of intersection.

c. Interpret the point of intersection in the context of the problem.

provate school in 2005
f(t)=85+18t

public school
g(t)=95+15t

graph
easy
replace g(t) and f(t) with y
y=18t+85
y=15t+95
input values for t and get values for y

y=18t+85
when t=0 y=85
when t=1 y=103
plot the oints (0,85) and (1,103)

y=15t+95
if t=0 then y=95
if t=1 then y=110
plot the points (0,95) and (1,110)

the easier way would just to be to solve the equatons but anyway
interscection point is (3 and 1/3,145)

so after 3 years (2008) it is about 145

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