Respuesta :
Answer:
 F = 0.792
Step-by-step explanation:
Given:
- The function C_o :
                C_o (t) = 90*(e^-0.3t - e^-2.5t)
- The function C_i :
                C_i (t) = 100*e^-0.3t
The function:
                [tex]F = UAC_o / UAC_i = \frac{\int\limits^n_0 {C_o} \, dt }{\int\limits^n_0 {C_i} \, dt }[/tex]
Find:
- The factor F.
Solution:
- Determine UAC_o from the function given:
            UAC_o = integral ( 90*(e^-0.3t - e^-2.5t) ) dt
            UAC_o = -300*e^(-0.3t) + 36*e^(-2.5t)
Evaluate integral from infinity to zero:
           | UAC_o | = 300 - 36 = 264
- Determine UAC_i from the function given:
            UAC_i = integral ( 100e-0.3t ) dt
            UAC_i = -333.333*e^(-0.3t)
Evaluate integral from infinity to zero:
           | UAC_i | =  0 + 333.333 = 333.3333
- Evaluate factor F:
             F =  | UAC_o | / | UAC_i |
             F = 264 / 333.3333
             F = 0.792
