Question

The populations P (in thousands) of a certain city from 2000 through 2007 can be modeled by P = 1674.7e^kt, where t represents the year, with t = 0 corresponding to 2000. In 2006, the population of the city was about 1,920,000. Find the Value of K

Answer 1

k = 0.02278

Explanation:

Given that:

The population P = 1674.7e^kt

where;

t represents the year,

if year 2000 represents t = 0

Then, the year 2007 represents = 7; &

year 2006 represents = 6

In 2006, population recorded in the city was about 1,920 thousand

Therefore;

`1920 = 1674.7e^{(k* 6)`

Taking the logarithm of both sides, we get:

`\mathtt{ In}(1920) = \mathtt{ In} ( 1674.7)+ 6k`

7.560080465= 7.423389324 + 6k

7.560080465 - 7.423389324 = 6k

0.136691141 = 6k

k = 0.136691141/6

k ≅ 0.02278