The smallest figurine in a gift shop is 2 inches tall. The height of each figurine is twice the height of the previous figurine. Write a power to represent the height of the tallest figurine. Then find the height.
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To represent the height of the tallest figurine, we can use a power. Let's denote the height of the smallest figurine as 2 inches and let's call the number of figurines "n".
Since the height of each figurine is twice the height of the previous figurine, we can express the height of the tallest figurine as:
2 * 2 * 2 * ... * 2
This can be simplified using exponential notation, where 2 is multiplied by itself "n" times:
2^n
To find the height of the tallest figurine, we need to determine the value of "n". Unfortunately, the number of figurines in the gift shop is not mentioned, so we cannot calculate the exact height without that information.
To represent the height of each figurine, we can use a power. Let's say the height of the first (smallest) figurine is represented by the base, and the height of the tallest figurine is represented by the power.
Let's assign variables to represent the heights:
- The height of the first (smallest) figurine = 2 inches
- The height of each figurine is twice the height of the previous figurine, so the height of the second figurine = 2 * 2 = 2^2
- The height of the third figurine = 2^2 * 2 = 2^3
- The height of the fourth figurine = 2^3 * 2 = 2^4
- And so on...
So, the power represents the number of times we multiply the base (2) to get the height of each subsequent figurine.
To find the height of the tallest figurine, we need to determine the value of the power.
Since the height of each figurine is twice the height of the previous figurine, we can see that the number of figurines we have is equal to the value of the power.
In this case, since we are given that there is a smallest figurine, we can assume there are at least two figurines (including the smallest one).
Therefore, the power needed to represent the height of the tallest figurine is the number of figurines minus one: n - 1.
In this case, n = 2 (the smallest figurine and another figurine), so the power is 2 - 1 = 1.
Therefore, the height of the tallest figurine = 2^1 = 2 inches.