6) The graph below shows the average savings, S thousands of dollars, of a group of university graduates as a function of t, the number of years after graduating from the university. The equation of the model can be expressed in the form S = at³ +bt² + ct + d, where a, b, c and d are real constants. 1 S 0 -5 1 3 2 -1 3 -5 A negative value of S indicates that a graduate is expected to be in debt. a) Write down one feature of this graph which suggests a cubic function might be appropriate to model this scenario. b) i) Write down the value of d. ii) Write down three simultaneous equations fro a, b, and c. iii) Hence, or otherwise, find the values of a, b, and c. c) Use the model to determine the total length of time, in years, for which a graduate is expected to be in debt after graduating from university.
6) The graph below shows the average savings, S thousands of dollars, of a group of university graduates as a function of t, the number of years after graduating from the university. The equation of the model can be expressed in the form S = at³ +bt² + ct + d, where a, b, c and d are real constants. 1 S 0 -5 1 3 2 -1 3 -5 A negative value of S indicates that a graduate is expected to be in debt. a) Write down one feature of this graph which suggests a cubic function might be appropriate to model this scenario. b) i) Write down the value of d. ii) Write down three simultaneous equations fro a, b, and c. iii) Hence, or otherwise, find the values of a, b, and c. c) Use the model to determine the total length of time, in years, for which a graduate is expected to be in debt after graduating from university.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:6) The graph below shows the average savings, S thousands of dollars, of a group of university
graduates as a function of t, the number of years after graduating from the university.
The equation of the model can be expressed in the form S = at³ + bt² + ct + d, where a, b, c,
and d are real constants.
1
S
0
-5
1
3
2
-1
3
i) Write down the value of d.
ii) Write down three simultaneous equations fro a, b,
and c.
-5
A negative value of S indicates that a graduate is expected to be in debt.
a) Write down one feature of this graph which suggests a cubic
function might be appropriate to model this scenario.
b)
iii) Hence, or otherwise, find the values of a, b, and c.
c) Use the model to determine the total length of time, in years,
for which a graduate is expected to be in debt after graduating from university.
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