Evaluating iterative formulas
I can evaluate and interpret iterative formula for various real-world situations.
- Year 11
Evaluating iterative formulas
I can evaluate and interpret iterative formula for various real-world situations.
Lesson details
Key learning points
- Iterative formulae use the previous iteration's output for this iteration's input
- A population can be estimated using an iterative formula
- Efficient use of the calculator makes this process much faster
Keywords
Iteration - Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration.
Common misconception
Some pupils want to clear their calculator display and type every single level of iteration in each time.
Encourage the pupils to trust their 'Ans' button. Get them to work on an example whereby they physically type the input value in and type the whole formula again. Then get them to repeat the same question using the 'Ans' button. Time this if you can!
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Iteration is the __________ application of a function or process in which the output of each iteration is used as the input for the next iteration.
Q2.If $$\text{f}(x)=4x-7$$ evaluate $$\text{f}(1)$$
Q3.If $$\text{f}(x)=4x-7$$ evaluate $$\text{fff}(1)$$
Q4.$$£30\;000$$ is invested at a rate of $$3.25$$% interest for $$4$$ years. Which calculation will work out the value of the investment after $$4$$ years?
Q5.Match the functions to the correct iterative formula we would use if we were to perform multiple repetitions of the same function.
$$\text{f}(x)=3x-7$$ - $$x_{n+1}=3x_{n}-7$$
$$\text{f}(x)=3x^2-7$$ - $$x_{n+1}=3(x_{n})^2-7$$
$$\text{f}(x)=3x^2-7x$$ - $$x_{n+1}=3(x_{n})^2-7(x_{n})$$
$$\text{f}(x)=x^3-7$$ - $$x_{n+1}=(x_{n})^3-7$$
$$\text{f}(x)=x^3-7x^2$$ - $$x_{n+1}=(x_{n})^3-7(x_{n})^2$$
Q6.$$£150$$ is invested at a rate of $$5.5$$% compound interest p.a. After how many years will the savings first be worth $$£500$$? years.
Assessment exit quiz
6 Questions
Q1.Iteration is the repeated application of a function or process in which the of each iteration is used as the input for the next iteration.
Q2.Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_1$$
Q3.Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_5$$
Q4.Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_2$$
Q5.Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_4$$
Q6.There are $$20\;000$$ fish in a lake. Every year $$4000$$ fish are fished and removed. The remaining population reproduces and grows by $$12$$%. After how many years will the stock of fish reach zero?
