𝑁(𝑡)=11.9𝑡3+20.3𝑡2+22𝑡+757

Question

The opening value of a stock index on the first day of trading from 1994 to 2010, can be modeled using the following polynomial: 𝑁(𝑡)=11.9𝑡3+20.3𝑡2+22𝑡+757,where 𝑡 is time in years since 1994. 

A) Graph this function in an appropriate window for years 1994-2010, label completely. 

B) What is the vertical intercept (𝑦-intercept), and what does this tell you in practical terms? 

C) Based on this model, what was the opening value stock index on the first day of trading in 2004? (15,108 is the actual number for that year).

Answer 1

a) That is a graphing problem from t = 0 to t = 16, so if you have no graphing calculator, you would have to evaluate the problem from t = 0 to t = 16 and then plot the points manually. y-axis would be stock index and x-axis would be the time in years.

b) Remember that to find the y-intercept of a function, the x value has to equal 0, so when t = 0 (year 1994), what does N(t) equal and what does it represent? (Hint: any variable above with t in it would automatically become 0 because t = 0)

c) what t value is 2004? Remember that t = 0 is 1994, so simply subtract 1994 from 2004 to get t = 10. Evaulate.