Question

Population figures of a city (in Lakhs) are as given below. Fit a exponential curve of the type y = ab^x and estimate the pupulation for the year 213.

Answer 1

The exponential. Logarithmetic equation is y = ab^x taking lagarithm on both side logy – log at x. log b.

The normal equations are:- n log a + log b. 

Σx = Σ log y ......(1) 

log a lx + log b. Σx² = Σx logy.......(2)

use deviation method and Σx = 0 let x and y be the year and population.

From (1) since Σx = 0:

loga = 1.0076 

a = Antilog (1.0076)= 10.1765.

log b = 0.08684

b = A.L(0.0868) = 1.2212

The exponential trend equation is:- y = ab^x

ŷ = 10,1765(1.2212)^x

ŷ(2013)= 10.1-765 (1-.2212)⁴

Here x = 4 for the projected value for 2013 

ŷ(2013) = 10.1765(2.2240) = 22.63 Lakhs.