Question

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?

Answer 1

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

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

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.