dictetzqh

2021-11-15

The analysis of accidents which happen per year is the average of the number of accidents which occurred in the 2 previous years

a) Calculate a recurrence relation for

b) Considering that three hundred thousand accidents occurred in year two and hundred thousand accidents occurred in year one, calculate the value for

Note: Both questions asked are different.Kindly read carefully

Alfonso Miller

Beginner2021-11-16Added 20 answers

Step 1

Part (a)

Let$A}_{n$ be the number of accidents happened in year x named as $a}_{n$ and $a}_{n-1},\text{}{a}_{n-2$ are the number of accidents that happened in two preceding two years.

Then according to question,

$a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2$

Therefore, the recurrence relation is$a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2$

Step 2

Part (b)

Substitute$300,00$ for $a}_{n-1$ and $100,000$ for $a}_{n-2$ in the equation

$a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2$

to calculate the value of$a}_{n$

$a}_{n}=\frac{300,000+100,000}{2$

$=200,000$

Therefore, the value of$a}_{n$ is 200,000

Part (a)

Let

Then according to question,

Therefore, the recurrence relation is

Step 2

Part (b)

Substitute

to calculate the value of

Therefore, the value of

22+64

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