Question

The largest doll is 12 inches tall. The height of each of the other dolls is 710 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.

The height of the smallest doll can be found using the expression

To the nearest tenth, the height of the smallest doll is
inches.

Answer 1

Expression for smallest doll: 12(7/10)^3

Explanation:

Since the largest doll is 12 inches, and we need to find the expression for the smallest one, we would multiply 12 and 7/10. Secondly, there are 4 dolls. We need to find the smallest doll's height, so it would be 7/10 times 7/10 times 7/10. Which could be simplified to (7/10)^3.

For the second question, just solve the expression and that is the height of the smallest doll.

Answer 2

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

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 0.7^3