Growth and Decay Modelling

What is a sequence in the context of growth and decay modelling?

• A mathematical equation with no pattern

• A series of numbers or events that follow a specific pattern or order.

• A type of plant or animal species

• A random assortment of numbers

Define recurrence relation and explain its significance in modelling growth and decay.

• A recurrence relation is an equation that recursively defines a sequence of values. It is significant in modelling growth and decay as it allows us to express the relationship between the current value and the previous values in a systematic way.

• A recurrence relation is a type of graph used to represent growth and decay.

• A recurrence relation is a linear equation that defines a sequence of values.

• A recurrence relation is a statistical method used to model growth and decay.

How do you model linear growth using recursion?

• Define a base case and a recursive case

• Ignore the base case and only use the recursive case

• Define two base cases

• Use a for loop

What is the explicit rule for linear growth and how is it used in modelling?

• y = ab^x

• y = mx - b

• y = mx + b

• y = ax^2 + bx + c

How is geometric growth modelled in the context of recursion?

• Using a formula that involves multiplying the initial value by a constant factor at each step

• Using a formula that involves subtracting the initial value by a constant factor at each step

• Using a formula that involves dividing the initial value by a constant factor at each step

• Using a formula that involves adding the initial value at each step

What is the explicit rule for geometric growth and how is it utilized in modelling?

• P(t) = P0 * (1 + r)^t

• P(t) = P0 / (1 - r)^t

• P(t) = P0 + rt

• P(t) = P0 * e^(rt)

Describe the explicit rule for geometric decay and its role in modelling growth and decay.

• A = A0 + r^n

• A = A0 - r^n

• A = A0 * r^n

• A = A0 / r^n

The first five terms of a sequence are 3, 7, 15, 31, 63 The recurrence relation that generates this sequence could be:

• B0 = 3, Bn+1 = Bn + 4

• B0 = 3, Bn+1 = Bn + 8

• B0 = 3, Bn+1 = 3Bn − 1

• B0 = 3, Bn+1 = 4Bn − 5

• B0 = 3, Bn+1 = 2Bn + 1

The following recurrence relation can generate a sequence of numbers A0 = 15, An+1 = An + 4 The number 51 appears in this sequence as:

• A1

• A7

• A8

• A9

• A10

A sequence of numbers is generated by the recurrence relation shown below A0 = 3, An+1 = 4An + 1 The value of A4 is:

• 3

• 4

• 13

• 213

• 853