Over time, the number of organisms in a population increases exponentially the table below shows the approximate number of organisms after y years.

the environment in which the organism lives can support at most 600 organisms. assuming the trend continues, after how many years will the environment no longer be able to support the population ?

a)12
b)24
c)61
d)82

We write the generic form equation:
 y = A (b) ^ t
 We must use two points in the table to find the constants A and b
 We have then:
 For: t = 1, y = 55
 55 = A (b)
 For: t = 2, y = 60
 60 = A (b) ^ 2
 We solve the system of equations:
 We divide both equations:
 (60 = A (b) ^ 2) / (55 = A (b))
 ((60) / (55)) = b
 b = 1.091
 We substitute in any of the equations:
 55 = A (b)
 55 = A (1,091)
 A = (55) / (1,091)
 A = 50.41 
 The equation that models the problem is:
 y = 50.41 * (1.09) ^ t
 For t = 29 we have:
 y = 613.5996987 (> 600)
 
 Assuming the trend continues the environment will not last until the population after 24 years.
 
 B) 24