I am having no luck solving this

Question

The population of Sasquatch in Portage County is modeled by the function

P(t)=150t/t+10

where t=0 represents the year 1803. When were there fewer than 100 Sasquatch in the county?

Answer 1

There is a another way of looking at this problem.  What number would be less than 100 people?  The answer is 99 people.  Substitute into the equation:  P(t)= (150*t)

                                                                 (t+10)         

 

                                                        Let P(t)=99   

                                                        99=  (150t)       Multiply both sides of the equation by (t+10)

                                                                 (t+10)

   

                                                      99(t+10)= (150t)     Use the Distributive property a(c+d)=ac+ad

                                           

                                                     99t+99(10)=150t

                                          

                                                     99t +990=150t           Subtract 99t from both sides of the equation

                                     

                                                     990=150t-99t

                                    

                                                     990=51t                   Now divide both sides by the number next to "t."

                                      

                                                     990/51  =t=19.4117647059 years  This is about 19 years.

 

To finish the problem, just add 19 years on to the date 1803.            

Answer 2

We can represent this by plugging in 100 for the P(t) side and using the > operator to represent when the population was less than this number and solve:

 

100 > 150t/t+10

 

100(t+10) > 150t  (multiply both sides by (t+10) to remove the fraction)

 

100t + 1000 > 150t  (distribute)

 

1000 > 50t  (subtract 100t from both sides)

 

20 > t  (divide both sides by 50)

 

t < 20  (rewrite with variable on left side)

 

Since t represents the years since 1803, this means that from 1803 (when 0 were living there) until 1822 (19 years later) there were fewer than 100 Sasquatch in the county.  You can check the answer by finding P(20) (which would be 1823): 150*20/(20+10), which is 3000/30, which reduces to 100.

 

Hope this helps!