本题目来源于试卷: IB MAI HL Functions Topic 2.4 Transformations，类别为 IB数学
[问答题]
A company that produces electronic components is investigatipvj hq+;8u av9 okc73bng7inxm9z h ,.mflyb-l 4t)2be o the heating properties of a particular component. The company finds that the temperature, T, of the component )m9myx-2bilf4 e.th,zln7b o can be modelled by the function
T(t)=$−40(0.9)^t$+90
where T is measured in degrees Celsius and t is measured in minutes of use.
1.Write down the initial temperature of the component.
2.Sketch a graph of T against t for 0≤t≤90.
3.Find the temperature of the component after 15 minutes.
4.Find the steady-state temperature of the component after a long duration of use.
To slow down the heating speed of the component, the company increases the size of the component in such a way that the component heats $\frac{3}{4}$ times as fast as the initial component.
5.Find a model for the temperature $T_2$ of the modified component.
Another option to reduce the rate of heating - instead of increasing the size of the component - is to add a thermal pad to the component. In this case the component heats half as fast as the initial component.
6.Find a model for the temperature $T_3$ of the component with the thermal pad.
7.Find the time taken for the component with the thermal pad to reach $80^{\circ}C$.
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