Following are the population of a district Year (x) 1881 1891 1901 1911 1921 1931 Population (y)Thousands 363 391 421 - 467 501 Find the population of the year 1911 - Business Mathematics and Statistics

Following are the population of a district

Year (x)	1881	1891	1901	1911	1921	1931
Population (y) Thousands	363	391	421	-	467	501

Find the population of the year 1911

योग

Since only five values of fix) are given, the polynomial which fits the data is of degree four.

Hence fifth differences are zeros.

i.e. Δ⁵y₀ = 0

(E – 1)⁵y₀ = 0

(E⁵ – 5E⁴ + 10E³ – 10E² + 5E – 1)y₀ = 0

E⁵y₀ – 5E⁴y₀ + 10E³y₀ – 10E²y₀ + 5Ey₀ – y₀ = 0

y₅ – 5y₄ + 10y₃ – 10y₂ + 5y₁ – y₀ = 0

501 – 5(467) + 10(y₃) – 10(421) + 5(391) – 363 = 0

2456 – 6908 + 10y₃ = 0

– 4452 + 10y₃ = 0

⇒ 10y₃ = 4452

y = `4452/10` = 445.2

The population of the year 1911 is 445.2 thousands

shaalaa.com

Finite Differences

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

अध्याय 5: Numerical Methods - Exercise 5.1 [पृष्ठ ११२]

अध्याय 5 Numerical Methods
Exercise 5.1 | Q 7 | पृष्ठ ११२

Evaluate Δ(log ax)

If f(x) = x² + 3x than show that Δf(x) = 2x + 4

Find the missing entries from the following.

x	0	1	2	3	4	5
y = f(x)	0	-	8	15	-	35