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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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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

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