Question

The largest doll is 12 inches tall. the height of each of the other dolls is 710710 the height of the next larger doll. write an expression involving a power for the height of the smallest doll. then evaluate the expression to find the height of the smallest doll to the nearest tenth of an inch.

Answer 1

the question doesn't say how many dolls. there would be an infinite number.  
But we'll just form the equation for the nth doll.     
 Largest doll = 12 inches
 2nd doll = (12) x 0.7
 3rd doll = (12 x 0.7) x 0.7
 4th doll = [(12 x 0.7) x 0.7) x 0.7 
  
 OK, We now see the pattern. Each successive doll is mult by the previous

doll height x 0.7
 the Nth doll, 12 is mult by 0.7(n-1)  
 So, the height of the nth doll can be expressed as: 12 x 0.7(n-1)  
 example: 4th doll = 12 x 0.7(4-1) = 12 x 0.73
  10th doll = 12 x 0.7(10-1) = 12 x 0.79 etc