Question

The largest doll is 12 inches tall. The height of each of the other dolls is 7/10 the height of the next larger doll. Write an expression involving a power that represents the height of the smallest doll. What is the height of the smallest doll?

Answer 1

The height of the tallest doll = 12 inches

The height of 2nd doll = 12×7/10

The height of 3rd doll = 12×7/10×7/10 = 12×(7/10)²

The height of 4th doll = 12×7/10×7/10×7/10 = 12×(7/10)³

Therefore the height of the smallest doll = 12×
`7/10^((n-1))`

where n is the number of dolls

So, if there are 5 dolls then the height of the smallest doll will be

12×
`7/10^((5-1))` = 12×
`7/10^(4)` = 2.8812 inches