College Algebra

Question

The population of a small town in central Florida has shown a linear decline in the years 1994-2006. In 1994 the population was 47400 people. In 2006 it was 38160 people.

A) Write a linear equation expressing the population of the town, P, as a function of t, the number of years since 1994.

Answer 1

2006 - 1994 = 12

So we have two points--(0, 47400) and (12, 38160). Now to use the slope formula to find that:

^{47400 - 38160} / _{0 - 12} = ⁹²⁴⁰/_-12 → -770

 

So we have the slope, and one of the town's population will be the b. In the equation
t(P) = mp + b, I'll leave it to you to put all the pieces together where.

Answer 2

THIS IS not A DIFFICULT QUESTION. BECAUSE THE DECLINE IS LINEAR AS OPPOSED TO EXPONENTIAL. THE FORM WILL BE P1=P0-LOSS IN ONE YEAR TIMES THE NUMBER OF YEARS.

 

P of the year=Original population-770x where x is the number of years.Now you can predict the population in any year.

 

47,400-38,160/12=770.

Population in 2010=47,400-770 times 16 years

 

The key is to note is the decrease is LINEAR, not exponential!

I hope this helps! Bruce