Respuesta :
The total value of Nokia's revenues at the end of 2003, if it had invested its revenues at 7% compounded continuously, would have been approximately 160 billion euros.
We follow these steps to arrive at the answer.
We have the revenue equation as:
[tex] r(t) = -1.7t^{2} + 5t + 28 [/tex]
When we substitute t as -1, 0, 1, 2 and so on in the revenue function above, the answer will be in billion euros.
We will assign values to 't' based on the year and information given in the question and solve the equation as follows:
Year t [tex] -1.7t^{2} [/tex] + 5t + 28 = Revenues (billions of Euros)
1999 -1 -1.70 -5 28 21.30
2000 0 0.00 0 28 28.00
2001 1 -1.70 5 28. 31.30
2002 2 -6.80 10 28 31.20
2003 3 -15.30 15 28 27.70
Since Nokia has invested its revenues at 7% compounded continuously, we use the formula:
[tex] Future Value = Revenues * {e^{rt}} [/tex]
in order to compute the value of revenues at the end of 2003. In this part of the question, we have to recognise that Nokia would have invested 1999 revenues for 4 years till the end of 2003. So 't' for the formula above will be 4. On the same basis, the values revenues at the end of 2003 is calculated. The value of e is taken as 2.71828
Year Revenues t [tex] {e^{rt}} [/tex] FV Revenues
1999 21.30 4 [tex] {2.71828^{0.07*4}} [/tex] = 1.32 28.18
2000 28.00 3[tex] {2.71828^{0.07*3}} [/tex] = 1.23 34.54
2001 31.30 2[tex] {2.71828^{0.07*2}} [/tex] = 1.15 36.00
2002 31.20 1[tex] {2.71828^{0.07*1}} [/tex] = 1.07 33.46
2003 27.70 0[tex] {2.71828^{0.07*0}} [/tex] = 1.00 27.70
The sum of the 'FV Revenues' column will give us the value of Nokia's revenues as 159.89 billion euros, which when rounded off to the nearest 10 billion euros gives 160 billion euros.
