You have chosen one ball; now you will predict how high it bounces on the 10th bounce. In this assignment, you may work alone, with a partner, or in a small group. Discuss the results of your work and/or any lingering questions with your teacher.
1.
Circle the ball you chose. (1 point)

Basketball
Tennis ball
Table-tennis ball

What do you know- The information on the basketball
What do you want to find out- How high it will bounce on its 10th bounce
What do you expect to find out- How high it bounces on its 10th.
Writing an Equation
2.
Assume that the ball rebounds the same percentage on each bounce. Using the initial drop height and the height after the first bounce, find the common ratio, r.
Note: Round r to three decimal places. Use this formula:

(3 points: 2 points for showing your work, 1 point for the answer)

r =
3.
State the general version of the recursive formula. (1 point)

4.
Find the recursive formula for the height of your ball. Remember that the 1st term, a1, is the height of the ball on the first bounce.(2 points)

5.
Fill out the following table for your ball's height after the first 3 bounces. Note: Let n = bounce number. The height on the 1st bounce, n = 1, is given. (2 points:)

Bounce
n
Height
First bounce
1
Basketball: 54 inches
Tennis ball: 58 inches
Table-tennis ball: 26 cm
Second bounce
2

Third bounce
3

6.
Write the explicit formula for the geometric sequence of the height of the ball on the nth bounce. Use the formula an = a1 • rn – 1. Remember that the 1st term, a1, is the height of the ball on the first bounce. (2 points)

Solving the Problem
7.
Using the explicit formula, find the height of the ball on the 10th bounce. (4 points: 2 points for showing your work, 2 points for the answer)

Taking Time to Reflect
8.
What are some factors that could affect the ball's bounce? Why might a ball bounce higher or lower than the regulated height? (1 point)

9.
For the sport you chose, why would it matter if a player used a ball that bounced higher than the regulation? (1 point)

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

how do heroes resolve conflicts in beowulf?

question 15 options:

they sue each other in court

they get a mediator

the seek counseling

they get even or take revenge

step-by-step explanation:

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.