According to Wikipedia, the International Basketball Federation (FIBA) requires that a basketball bounce to a height
of 1300 mm when dropped from a height of 1800 mm.
a. Suppose you drop a basketball and the ratio of each bounce height to the previous bounce height is 1300:1800.
Let h be the function that assigns to n the bounce height of the ball (in mm) on the nth bounce. Complete the chart
below, rounding to the nearest mm.
n
h(n)
0
1
1800
2
3
b. Write a function that could find the height of the next bounce if you know the height of the current bounce.
c. Write a function that could find the height of any bounce without knowing the height of the bounce before it.
d. Using your equation for part c, find the height of the 8th bounce.
According to Wikipedia, the International Basketball Federation (FIBA) requires that a basketball bounce to a height
of 1300 mm when dropped from a height of 1800 mm.
a. Suppose you drop a basketball and the ratio of each bounce height to the previous bounce height is 1300:1800.
Let h be the function that assigns to n the bounce height of the ball (in mm) on the nth bounce. Complete the chart
below, rounding to the nearest mm.
n
h(n)
0
1
1800
2
3
b. Write a function that could find the height of the next bounce if you know the height of the current bounce.
c. Write a function that could find the height of any bounce without knowing the height of the bounce before it.
d. Using your equation for part c, find the height of the 8th bounce.
©Relevantmathematics.com
Geometric Sequences - Student
1
Card Set: Situations
S1
S2
A culture of bacteria swabbed from a toilet seat has
A biologist is observing a group of 600 cells. She
150 of a particular bacteria on it. That particular
notices that, after two hours, each of the 600 cells
bacteria doubles every 2 hours.
divided into two cells. Then, two hours later, each of
those 1200 cells divided into two cells.
S3
S4
A batch of bacteria is growing in a Petri dish. There are
100 cells to begin with and this specific bacteria
doubles every hour.
S5
S6
A science lab is working with a radioactive element
A population of penguins started with 100 penguins.
that has a half-life of 1 day. That means, after 1 day,
The next month, there was an increase of 300
half of the remaining substance disintegrates. The lab
penguins. The next month there was an increase of
has 600 mg of the substance.
1200 penguins. The next month, there was an increase
of 4800 penguins.
S7
S8
A sequence is shown below.
A geometric sequence is shown below.
1
-3, -9, -27, -81, ...
/8, 1/4, 1/2, 1, ...
S9
S10
A sequence is shown below.
A population of rabbits is observed every month. The
7, 35, 175, 875, ...
first month there were 100 rabbits. The second month
there were 300 rabbits, the third month there were 900
rabbits.
©Relevantmathematics.com
Geometric Sequences - Student
2
Card Set: Recursive Functions
RF1
RF2
Let n =
Let f(n) =
f(1) = 1/8
f(n + 1) = 2 · f(n) for integers n ≥ 2
RF3
RF4
Let n =
Let n =
Let f(n) =
Let f(n) =
f(1) = -3
f(1) = 100
f(n) = 3f(n - 1) for integers n ≥ 2
f(n+1) = 4f(n) for integers n ≥ 2
RF5
RF6
Let n =
Let n =
Let f(n) =
Let f(n) =
f(1) = 600
f(1) = 1/8
f(n + 1) = 2 · f(n) for integers n ≥ 2
f(n + 1) = 0.5 · f(n) for integers n ≥ 2
RF7
RF8
Let n =
Let n =
Let f(n) =
Let f(n) =
f(1) = 100
f(1) = 150
f(n + 1) = 2 · f(n) for integers n ≥ 2
f(n) = 2f(n - 1) for integers n ≥ 2
RF9
RF10
Let n =
Let n =
Let f(n) =
Let f(n) =
f(1) = 600
f(1) = 7
f(n + 1) = 1/2 · f(n) for integers n ≥ 2
f(n + 1) = 5 · f(n) for integers n ≥ 2
©Relevantmathematics.com
Geometric Sequences - Student
3
Card Set: Explicit Functions
EF1
EF2
f(n) = -3 · 3n for integers n ≥ 1
f(n+1) = 100 · (4)n for integers n ≥ 1
EF3
EF4
f(n+1) = 100 · (3)n for integers n ≥ 1
f(n) = (2)(n-1) · (1/8) for integers n ≥ 1
EF5
EF6
f(n+1) = 600 · (1/2)n for integers n ≥ 1
f(n) = 2(n-1) · 150, for integers n ≥ 1
EF7
EF8
1
f(n) = ( /2)
(n-1)
· ( /8) for integers n ≥ 1
1
EF9
EF10
f(n) = 2(n-1) · 100 for integers n ≥ 1
f(n+1) = 7 · (5)n for integers n ≥ 1
©Relevantmathematics.com
Geometric Sequences - Student
4
Follow-up Lesson: Two Situations
The number of bacteria in a Petri dish after different amounts of time are listed in the table below.
Day
Number of Bacteria
1
200
2
400
3
800
4
1,600
a. Write a recursive function that models the number of bacteria in the dish after x days.
b. Write an explicit function that models the number of bacteria in the dish after x days.
Sodium-24 has a half-life of 15 hours. That is, every 15 hours, half of the remaining amount disintegrates. If you
have 64 grams of Sodium-24,
a. Write a recursive rule to represent this situation.
b. Write an explicit rule to represent this situation.
c. Using both of your rules, how many grams will be left after 75 hours?
©Relevantmathematics.com
Geometric Sequences - Student
5