The annual net sales (revenue) earned by the Finnish cell phone company Nokia from January 1999 to January 2003 can be approximated by $R ( t ) = - 1.7 t ^ { 2 } + 5 t + 28$ billion euros per year $( - 1 \leq t \leq 3 )$ where t is time in years ( $t = 0$ represents January 2000). Estimate, to the nearest billion, Nokia's total revenue from January 1999 through December 2002.
A)Total revenue 116 billion euros
B) Total revenue 120 billion euros
C) Total revenue 91 billion euros
D) Total revenue 4 billion euros
E) Total revenue 20 billion euros

Question

The annual net sales (revenue) earned by the Finnish cell phone company Nokia from January 1999 to January 2003 can be approximated by $R ( t ) = - 1.7 t ^ { 2 } + 5 t + 28$ billion euros per year $( - 1 \leq t \leq 3 )$ where t is time in years ( $t = 0$ represents January 2000). Estimate, to the nearest billion, Nokia's total revenue from January 1999 through December 2002.  
A)Total revenue   116 billion euros
B) Total revenue   120 billion euros
C) Total revenue   91 billion euros
D) Total revenue   4 billion euros
E) Total revenue   20 billion euros

Quizplus · Accepted Answer

To estimate Nokia's total revenue from January 1999 through December 2002, we integrate the given revenue function $R(t) = -1.7t^2 + 5t + 28$ over the interval $[-1, 3]$. The integral gives the total revenue over these years. The exact calculation of the integral is not provided, but the correct choice is the one that approximates this calculation to the nearest billion euros, which is option A.

The Annual Net Sales (Revenue) Earned by the Finnish Cell R(t)=−1.7t2+5t+28R ( t ) = - 1.7 t ^ { 2 } + 5 t + 28R(t)=−1.7t2+5t+28

The Annual Net Sales (Revenue) Earned by the Finnish Cell $R ( t ) = - 1.7 t ^ { 2 } + 5 t + 28$