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.

Evaluating iterative formulas

Maths

Checking and securing understanding of compound interest calculations

Building on composite functions

Approximating solutions to equations

Signs of a solution

Problem solving with iteration

In this unit, pupils continue to explore composite functions, thereby building on their work from the prior unit. Pupils need to understand function notation from the prior unit as this is used in iteration.

In this unit, pupils continue to explore composite functions and develop understanding of iteration, building on their work on functions and proof.

Iteration

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.

Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_1$$ {{}}

Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_5$$ {{}}

Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_2$$ {{}}

Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_4$$

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?

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.

If $$\text{f}(x)=4x-7$$ evaluate $$\text{f}(1)$$

If $$\text{f}(x)=4x-7$$ evaluate $$\text{fff}(1)$$

$$£30\;000$$ 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?

Match the functions to the correct iterative formula we would use if we were to perform multiple repetitions of the same function.

$$£150$$ is invested at a rate of $$5.5$$% compound interest p.a. After how many years will the savings first be worth $$£500$$? {{}} years.

Evaluating iterative formulas

Lesson outcome