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QLDSpecialist MathematicsQuick questions

Unit 4: Further calculus, and statistical inference

Quick questions on Growth, decay, cooling and logistic models in QCE Specialist Mathematics Unit 4

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is interpreting the constant kk?
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The constant kk sets the timescale: a larger ∣k∣|k| means faster change. Solve for kk using a second data point (for example a known value at a later time) when the scenario provides one.
What is model?
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Newton's law of cooling gives T=Ts+(T0−Ts)e−ktT = T_s + (T_0 - T_s)e^{-kt} with Ts=20T_s = 20, T0=90T_0 = 90:
What is use the 5-minute reading to find kk?
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At t=5t = 5, T=60T = 60:
What are temperature at 10 minutes?
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Note e−10k=(e−5k)2=(47)2=1649e^{-10k} = (e^{-5k})^2 = \left(\frac{4}{7}\right)^2 = \frac{16}{49}:
What is check?
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The coffee dropped 30∘30^\circ in the first 5 minutes and about 17∘17^\circ in the next 5, a slowing decline as it nears the 20∘20^\circ room temperature, exactly as Newton's law predicts.

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