Question

Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2014?

Answer 1

Answer:

Tacoma's population in 2014 will be 587,439 people

Step-by-step explanation:

we know that

The equation of a exponential growth function  is given by the formula

$y=a(1+r)^x$

where

y is Tacoma's population in thousand

x is the number of years since 2000

r is the rate of change

a is the initial value

we have

$a=200\\r=8\%=8/100=0.08$

substitute

$y=200(1+0.08)^x$

$y=200(1.08)^x$

what will Tacoma's population be in 2014?

Find the value of x

$x=2014-2000=14\ years$

substitute the value of x

$y=200(1.08)^{14}=587.439\ thousand$

therefore

Tacoma's population in 2014 will be 587,439 people