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

Name Date

The approach model Problem set B

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

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. In the model \(D=a+bk^{-t}\) with \(a=18\), the starting value is \(D(0)=4\). Find b.

  2. A model is \(D=14+bk^{-t}\) with \(k>1\), \(D(0)=0\) and \(D(1)=12.6\).

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

  3. A model is \(D=30-30\times1.3^{-t}\), with D in km and t in hours. Find the distance still to travel after 6 hours.

  4. The graph shows \(D=a+bk^{-t}\) with \(k>1\). The dashed line is \(D=15\). Explain why a is the total distance travelled, and write its value.

    24681051015t (hours)D (km)D

In context

  1. A skateboarder rolls towards a barrier 9 m from the start of a ramp. Her distance from the start after t hours is D m, where \(D=a+bk^{-t}\) and \(k>1\). She starts at the top, so \(D(0)=0\), and after 1 hour \(D(1)=6.3\).

    1. (a) State the value of a.
    2. (b) Find b.
    3. (c) Find k.
    4. (d) Find the distance still to go after 4 hours.
    5. (e) Find the time, to the nearest hour, when D = 8.8.

Stretch

  1. A weather balloon rises towards a cloud layer. Its height above the launch point after t hours is D m, where \(D=15+bk^{-t}\) with \(k>1\). It starts at the launch point, and after 2 hours its height is 11.25 m.

    1. (a) Find k.
    2. (b) Find the time, to the nearest hour, when D = 14.5.

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