The formula A = 146e0.03t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 229 thousand?

So it will take 15 year from 1998 to reach population 229 thousands.

i. e. In 2013 population will be 229 thousand.

Step-by-step explanation:

Given:

Formula model population for city A=146e0.03t

To Find:

Years required to reach population 229 thousands after 1998

Solution:

Using the model,

A=146e0.03t

here A=229

So equation becomes,

229=146e0.03t

(229/146) = e0.03t

Using log function with base 10 on both sides we get,

Log (229/146) = log (e^0.03t)

log (1.56489) = 0.03tlog (e) ... (using log property log (a^n) = nloga)

0.19548=0.03*t*0.43429

0.19548/0.013028=t

t = (0.19548/0.013028)

t=15.01

t=15 years

So it will take 15 year from 1998 to reach population 229 thousands.