P = (0.16)t^2 +7.2t + 100 where p is population in thousands  and year 2000 is

represented by t = 0.;

a) In 2010 t = 10 and P = [(0.16)(10)^2+7.2(10)+100]*(10^3) = 188,000.

b) In 1995 t = - 5 and P = [(0.16)( -5)^2+7.2(-5)+100]*(10^3)  =   68,000.

c) When   t  = - a, P = [(0.16)(-a)^2+7.2(-a)+100] = (0.16)a^2 -7.2a +100 = 52.

Then 16a^2-720a+10,000 = 5,200, ie., a^2-45a+300 = 0, 2a = 45(+/-)D, where

D^2 = 45^2 = 4*1*300 = 2025-1200 = 825. Then D = (+/-) 28.72281323 & a =

8.138593384 or 36.86140662. Reject larger root. t = -8 ---> P = 52.64(10^3).  

Around October 10/1991, population reached 52,000.

 Suppose that the population of a town is given by 

 P = 0.16t^2 + 7.2t + 100 

 where P is the population in thousands 

 and t is the time in years, 

 with t = 0 representing the year 2000.

 a) 

 The population in 2010 was 188,000.

 b) 

 The population in 1995 was 68,000.

 c) 

 The population was 52,000 in 1992.

Didn't you just ask this recently? 

You are given:

P = 0.16t² + 7.2t + 100

With "t" meaning the number of years after 2000 and "P" is in thousands.

So what's the population in 2010?  Solve for P when t = 10:

P = 0.16t² + 7.2t + 100

P = 0.16(10)² + 7.2(10) + 100

P = 0.16(100) + 7.2(10) + 100

P = 16 + 72 + 100

P = 188

The population was 188,000 in 2010.

What's the population in 1995?  Solve for P when t = -5:

P = 0.16t² + 7.2t + 100

P = 0.16(-5)² + 7.2(-5) + 100

P = 0.16(25) + 7.2(-5) + 100

P = 4 - 36 + 100

P = 68

The population was 68,000 in 1995.

When will the population reach 52,000?  Solve for t where P = 52

P = 0.16t² + 7.2t + 100

52 = 0.16t² + 7.2t + 100

Divide both sides by 0.16 to simplify things a little:

325 = t² + 45t + 625

0 = t² + 45t + 300

Quadratic equation:

t = [ -b ± √(b² - 4ac)] / (2a)

t = [ -45 ± √(45² - 4(1)(300))] / (2 * 1)

t = [ -45 ± √(2025 - 1200)] / 2

t = [ -45 ± √(825)] / 2

t = (-45 ± 28.72281) / 2

t = -73.72281/2 and -16.27719/2

t = -36.861405 and -8.138595

Rounded to the nearest whole:

t = -37 and -8

The population was 52,000 in two years:

1963 and 1992