A new college predicts that its student body will grow rapidly at frst and then

Question

A new college predicts that its student body will grow rapidly at frst and then begin to level off according to the Gompertz aurve with equation Ns 10,0000 9 number of years after the college opens. a. What does this model predict the number of students to be when the college opens? N- (Do not round until the final answer. Then round to the nearest integer as needed) b. How many students are predicted to attend the college after 5 years? Nstudents (Do not round until the final answer. Then round to the nearest integer as needed) c. Graph the equation and estimate an upper limit on the number of students at the colenge. Choose the graph of the equation below 2 students,where t is tme O B. o c O 0, 0 c 10 What is the upper limt on the number of students at the college? Click to select your answerls)

Explanation / Answer

a) N = 10,000 ( 0.9)^3^t

when college starts that is t = 0

N = 10,000 ( 0.9)^3^0

N = 9000 students

b) after 5 years

N = 10,000 ( 0.9)^.3^5

N = 9997 students

c) option c graph is correct

d) upper limit is 10,000 students

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