In 1998 the population of a colony is 10000 and is decreasin

In 1998, the population of a colony is 10,000. and is decreasing exponentially at 1.5% per year. a) What will the population be after 5 years? b) In what year will there be half of the population left? In 2003, the population of a city is 80,000 people, and is growing at a rate of 47% per year. a) What will the population be in 2015? b) In what year will the population be triple?

Solution

12. We have to use the following formula

   P(t) = P₀(1-r)^t

P(t) is the population after t years

P₀ is the initial population

r is the rate

In this question P₀ =10000, r=1.5 %= .015 , t=5 yrs

a. P(5) =10000(1-.015)⁵

            = 10000 * .985⁵   = 9272

b. 5000=10000(1-.015)^t

    .5= .985^t

Taking log on both sides

log .5= t log .985

t= log.5/log .985

t= approx 46 yrs

13. We have to use the following formula here

      P(t) = P₀(1+r)^t

a.      t=2015-2003=12 yrs   , r=4%=.04

      P(t) = 80000(1+.04)¹²

              = 80000*1.04¹²

               = 128083

b.   We have to find the year in which the population be triple and triple means triple of 80000=240000

240000=80000(1+.04)^t

           3= 1.04^t

Taking log on both sides

        log3/log1.04=t

          t=28 yrs