Question

A town has a population of 17000 and grows at 2.5% every year. To the nearest year, how long will it be until the population will reach 19600?

Answer 1

Answer:

6 years

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

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

where

y ----> is the population

x ---> is the number of years since now

a ---> is the initial value or y-intercept

r ---> is the rate of change

we have

$a=17,000\ people$

$r=2.5\%=2.5/100=0.025$

substitute

$y=17,000(1+0.025)^x$

$y=17,000(1.025)^x$

For y=19,600

substitute in the exponential equation and solve for x

$19.600=17,000(1.025)^x$

$(19.600/17,000)=(1.025)^x$

apply log booth sides

$log(19.600/17,000)=log(1.025)^x$

$log(19.600/17,000)=xlog(1.025)$

$x=log(19.600/17,000)/log(1.025)=6\ years$