Solve the ODE below subject to the initial condition Q (0) = 131. Q′ (t) = k (Q-70) If Q represents the quantity of ice crystals measured over time, then calculate Q at t=1 seconds for k=-0.8 / second. Enter your answer in decimal notation (only). Round in the tenths place to give a fractional representation of a partly formed crystal (if any).

Question

Chemistry

Augustus Webb

17 May, 13:06

Solve the ODE below subject to the initial condition Q (0) = 131. Q′ (t) = k (Q-70) If Q represents the quantity of ice crystals measured over time, then calculate Q at t=1 seconds for k=-0.8 / second. Enter your answer in decimal notation (only). Round in the tenths place to give a fractional representation of a partly formed crystal (if any).

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Answers (1)

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Haleigh Gordon · Answer 1

Answer

Q (final) = 97.4090668112

Explanation:

dQ/dt = k (Q - 70)

dQ / (Q - 70) = kdt

In (Q (final) - 70) / (Q (initial) - 70) = kt

(Q (final) - 70) / (Q (initial) - 70) = e^ (kt)

Given that,

t = 1

k = 0.8

Q (initial) = 131

(Q (final) - 70) / (131 - 70) = e^ (1*-0.8)

(Q (final) - 70) / (61) = e^0.8

(Q (final) - 70) / (61) = 0.44932896411

Q (final) - 70 = 0.44932896411*61

Q (final) - 70 = 27.4090668112

Q (final) = 27.4090668112 + 70

Q (final) = 97.4090668112