Algebraic Word Problem

Question

A population has size 5000 at time t = 0, with t in years.

 

a.) If the population decreases by 200 people per year, find a formula for the population, P , at time t

 

 

b.) If the population decreases by 8% per year, find a formula for the population, P , at time t.

Answer 1

Hi Erin,

 

Below are our step-wise solutions for each problem:

 

 

Problem #1:

 

    1.  Our given info:

             (a)  5000 = initial population

             (b)  t = # of years

             (c)  -200t = decrease of 200 people per year

 

    2.  Our formula (P) at time (t):

             P = 5000 - 200t

 

 

Problem #2:

 

    1.  Our given info:

             (a)  5000 = initial population

             (b)  8% = 0.08

             (c)  (1 - 0.08)^t = decrease of 8% each year

             

    2.  Our formula (P) at time (t):

             P = 5000(1 - 0.08)^t

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.