Question

Please help it is due tomorrow.... I need help with 9, 11, and 12

Answer 1

The population is growing at the rate of 2% per year.
So in 'y' years from the start, its size is modeled by the function

             Population = (original size) x (1.02)^y power

This equation is familiar from all of the bank-interest problems.

9).  The population is 765 right now.  In 'y' more years from now, it will be

               Population = 765 x (1.02)^y power

11).  In 5 years from now, it will be  P = 765 (1.02)^5 = 845 students (rounded)

12).  The population will exceed 1,000 students when

               1,001 = 765 (1.02)^y

Divide each side by 765 :  1,001/765 = (1.02)^y

Take the log of each side:  log(1,001/765) = y log(1.02)

Divide each side by  log(1.02) :  y = log(1,001/765) / log(1.02)

Fire up your calculator and crank out that number:

log(1,001/765) / (log(1.02) = 0.11677 / 0.0086 = 13.5779 years


If the 2% growth is steady and uniform 24/7 throughout the year, then
this number means that the 1,001th student will enroll in

13 years 30 weeks 1 day 2 hours 6 minutes 36 seconds from right now.