Question

The revenue, in millionsmillions of dollars, for a company in year tt is given by the function: r(t)=15e0.19t,0≤t≤15 r(t)=15e0.19t,0≤t≤15 and the cost, in millions billions of dollars, to run the company in year tt is approximated by: c(t)=12e−0.03t,0≤t≤15 c(t)=12e−0.03t,0≤t≤15 where tt is the number of years after january 1st of the year 20002000. what was the net profit (in millionsmillions of dollars) for the company from january 1st in the year 20002000 until january 1st in the year 20072007

Answer 1

The net profit of the company in this case is given by the subtraction of the income minus the costs.
 We have then:
 b (t) = r (t) - c (t)
 b (t) = 15 * e ^ (0.19 * t) - 12 * e ^ (- 0.03 * t).
 We must determine the number of years.
 from january 1st in the year 2000 until january 1st in the year 2007:
 t = 2007-2000 = 7.
 We have then evaluating t = 7 in the function:
 b (7) = 15 * e ^ (0.19 * 7) - 12 * e ^ (- 0.03 * 7).
 b (7) = 46.99 millions of dollars
 answer:
 the net profit was 46.99 millions of dollars