Respuesta :
Answer:
Q(1) = 103.25
Step-by-step explanation:
Given:
- The rate of ice crystals formation/depletion is given by:
Q'(t) = k*(Q - 70)
- For the initial conditions;
Q(0) = 144 , k = -0.8 / sec
Find:
Calculate Q at t=1 seconds for k=−0.8 /second. Enter your answer in decimal notation (only).
Solution:
- First we will solve the differential equation to get a functions Q with time, Q(t).
- Use the given ODE:
dQ/ dt = -0.8*(Q - 70)
- Separate variables:
dQ / (Q - 70) = -0.8*dt
- Integrate both sides:
Ln | Q - 70 | = -0.8*t + C
- Use initial conditions to evaluate @ Q(0) = 144:
Ln | 144 -70 | = -0.8*0 + C
C = Ln | 74 |
- The Solution is given by:
Ln | (Q - 70) / 74 | = -0.8*t
Q(t) - 70 = 74*e^(-0.8*t)
Q(t) = 70 + 74*e^(-0.8*t)
- Now use the solution to the ODE and evaluate @ t = 1s
Q(1) = 70 + 74*e^(-0.8*1)
Q(1) = 103.25
