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The Exponential Monster

Back to the story:

For some reason, your science officer starts yelling crazy things at you (while waving her one arm all around) and quits.  In desperation, you promote the crew cook, Stu, and send him out of the cave to do more exploring.  Unfortunately, he finds a second species of drooling alien monster...  Fortunately for Stu, it's an herbivore!  Unfortunately for Stu, your uniforms are green.  Days later, one of Stu's socks and a clip board of growth data for the monster is found.

Here's what Stu had written:

SECOND ALIEN SPECIES IS 4 INCHES TALL AT BIRTH

TIME (t)HEIGHT IN FEET
 
At birth:    
     t = 0		4
After 1 hour: 
     t = 1		4 * 3 = 12
After 2 hours: 
     t = 2		4 * 3 * 3 = 4 * 3^( 2 ) = 36
After 3 hours: 
     t = 3		4 * 3 * 3 * 3 = 4 * 3^( 3 ) = 108
After 4 hours:
     t = 4		4 * 3 * 3 * 3 * 3 = 4 * 3^( 4 ) = 324
See a pattern yet?

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After 10 hours:
     t = 10

4 * 3^( 10 )

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Afterthours:

4 * 3^( t ) ... the 4 is the initial height ... the 3 is the growth rate ... the t is the time

CONCLUSION:  WITH EACH HOUR THAT PASSES, THE MONSTER
                           TRIPLES IN HEIGHT AND MAY BE TASTY BROILED
                           WITH ONIONS.

FORMULA FOR GROWTH:

h( t ) = 4 * 3^( t )