The local school district has studied trends in population g

The local school district has studied trends in population growth find has provided the following predictions for enrollment in two of their high schools. Current enrollment at Park Valley High School is 1750 students and the enrollment is expected to increase by 55 students per year. The current enrollment at Tisdale High School is 1630 students and the enrollment is expected to increase by 10% per year. How many students will be enrolled in park Valley High School 1 year since the prediction was made? Let f be a function that gives the number of students enrolled at Park Valley High School. P, in terms of the number of years, n, since the prediction was made. What is the rule for this function? Approximately how many students will be enrolled in Tisdale High School 1 year since the prediction was made\"\' (Remember you cannot have fractional parts of a student so round your answer up to the nearest integer.) Let g be a function that gives the number of students enrolled at Tisdale High School. T in terms of the number of years, n, since the prediction was made What is the rule for this fraction? Use function notation to express the following statements. The projected number of students enrolled at Tisdale High School 5 years after the prediction was made. The difference in the projected number of students enrolled at Park Valley High School from 3 years after the prediction was made to 3 years after the prediction was made.

Solution

a) Park valley school:

after 1 year since prediction no. of students = 1750 +55 = 1805

b) every no. of students increase by 55

So, P(n) = 1750 +n*55 = 1750 +55n

Linear function

c) no. of students at start = 1630

% increase = 10%

So, no. of students increased in 1 year= (10/100)*1630 = 163 students

Total no. of students enrolled after 1 year = 1630 +163 = 1793 students

d) g(n) = 1630(1.1)^n

exponential function

e) After 5 yrs : g(5) = 1630*(1.1)^5 = 2625 students

f) after 3 yrs ;P(3) = 1750 +55*3 = 1915 students