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IB Mathematics: Applications and Interpretation SL · 12.5: Functions · 12.5.5

Name Date

The approach model Problem set A

Show each step. Use Solve for t on the calculator, and round to the nearest hour only when asked.

Difficulty: first skills applying them stretch

Skills

  1. In the model \(D=a+bk^{-t}\) with \(a=15\), the starting value is \(D(0)=3\). Find b.

  2. A model is \(D=9+bk^{-t}\) with \(k>1\), \(D(0)=0\) and \(D(1)=7.2\).

    1. (a) Find b.
    2. (b) Find k.

  3. A model is \(D=20-20\times1.4^{-t}\), with D in km and t in hours. Find the distance still to travel after 5 hours.

  4. The graph shows \(D=a+bk^{-t}\) with \(k>1\). The dashed line is \(D=10\). Explain why a is the total distance travelled, and write its value.

    2468101214246810t (hours)D (km)D

In context

  1. A hiker walks towards a mountain hut 6 km from the start of the trail. Her distance from the start after t hours is D km, where \(D=a+bk^{-t}\) and \(k>1\). She starts at the trailhead, so \(D(0)=0\), and after 1 hour \(D(1)=3.6\).

    1. (a) State the value of a.
    2. (b) Find b.
    3. (c) Find k.
    4. (d) Find the distance still to go after 3 hours.
    5. (e) Find the time, to the nearest hour, when D = 5.9.

Stretch

  1. A submersible sinks towards a wreck. Its depth below the surface after t hours is D m, where \(D=12+bk^{-t}\) with \(k>1\). It starts at the surface, and after 2 hours its depth is 10.08 m.

    1. (a) Find k.
    2. (b) Find the time, to the nearest hour, when D = 11.5.

jmaths.xyz · AI SL · 12.5.5 Review: the approach model and graph transformations