I need help with an word problem using exponents

Question

the question is the largest doll is 12 inches tall.the hieght of each of the other dolls is 7/10 the height of the next larger doll.write an expression for the hieght of the smallest doll. what is the hieght of the smallest doll?

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.