SOLUTION: I'm not sure if this is the right category, but here's the word problem. "The population of butterflies in a local pasture is 60 in January 2010. In March 2010, the population o

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I'm not sure if this is the right category, but here's the word problem. "The population of butterflies in a local pasture is 60 in January 2010. In March 2010, the population o      Log On


   

Question 636312: I'm not sure if this is the right category, but here's the word problem.
"The population of butterflies in a local pasture is 60 in January 2010. In March 2010, the population of butterflies is 80. The population P of butterflies can be modeled by the equation P=ab^t where t is the number of months since January 2010 and a and b are constants.
A. Find the values of a and b in the model P=ab^t
B. According to the model, what will the population of butterflies be in January 2011?
C. According to the model, when will the population reach 200?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

P=ab%5Et , where t is the number of months since January 2010 (Jan 2010 t = 0, Feb t = 1, etc)

The population of butterflies in a local pasture is 60 in January 2010. a = 60

In March 2010, the population of butterflies is 80:  80 = 60b^2 , b+=+2%2Fsqrt%283%29

B. According to the model, what will the population of butterflies be in January 2011? t = 12

+P+=+60%282%2Fsqrt%283%29%29%5E12+=+337

 C. According to the model, when will the population reach 200? 

 +200+=+60+%282%2Fsqrt%283%29%29%5Et

 200%2F60+=+%282%2Fsqrt%283%29%29%5Et

  +log%28200%2F60%29%2Flog%282%2Fsqrt%283%29%29+=+.5229%2F.0625 = t = 8.38 or in the 9th month