One of the rides in the park sends the rider down a steep slide and over a series of hills that

Question

gradually decrease in height until the ride ends. Using the table below, create both a recursive and
an explicit geometric equation for the height of a given hill. Use your recursive equation to answer
the following question: if you increased the drop height to 400, what would be the height of the
fourth hill?
0
1
2
320
80
20
5
1.25

Answer 1

To create a recursive equation, we can observe that the height of each hill is one-fourth the height of the previous hill:

Recursive equation: H(n) = H(n-1) * (1/4)

Using this equation, we can find the height of the fourth hill:

H(4) = H(3) * (1/4)
= 20 * (1/4)
= 5

Therefore, the height of the fourth hill would be 5 units.

To create an explicit geometric equation, we can observe that each hill's height is equal to the initial drop height (h0) multiplied by the common ratio (r) raised to the power of the hill number (n):

Explicit geometric equation: H(n) = h0 * r^(n-1)

In this case, the initial drop height is 320, and the common ratio is 1/4:

H(n) = 320 * (1/4)^(n-1)

To find the height of the fourth hill using this equation:

H(4) = 320 * (1/4)^(4-1)
= 320 * (1/4)^3
= 320 * (1/64)
= 5

Again, the height of the fourth hill is 5 units.