1. Determine whether the sequence is arithmetic, geometric, or neither: 3, 6, 12, 24, …. *
arithmetic
geometric
neither
2. Write a function rule for the table. *
x f(x)
3 9
4 16
5 25
6 36
f(x) = x4 (x to the 4th power)
f(x) = x2 (x squared)
f(x) = 4 – x
f(x) = 4x
3. A zucchini plant in Maria's garden was 12 centimeters tall when it was first planted. Since then, it has grown approximately 0.3 centimeters per day.a. Write a rule to describe the function. *
H(d) = 0.3d + 12
12d + 0.3
H(d) = 0.3d
H(d) = 0.3 + 12
4. A sloth travels at a rate of 0.5 meters per minute. a. Write a rule to describe the function. b. How far will the sloth travel in 8 minutes? *
d(t) = 0.5t; b. 4 meters
d(t) = t + 0.5; b. 4.3 meters
d(t) = 0.5t + 1; b. 4.1 meters
d(t) = 0.5t; b. 4.2 meters
5. Which function is greatest at x = 2? *
6. Your family borrows $6,000 to buy a car. The car loan has a 5% annual interest. The loan is for five years. What is the total amount your family owes for the car? *
$1500
$7500
$15000
$6150
7. A faucet is leaking at a rate of 0.8 gallon per hour. Write a rule to find the volume of water that will leak in 3 hours. Let w represent the volume of water and let t represent the number of hours. *
8. Which of the following sequences is an arithmetic sequence? *
–1, 2, 5, 8, . . .
6, 9, 5, 8, 4, 7, . .
5, 20, 80, 320, . .
100, 10, 0.1, 0.01, . .
That's pretty cool
1. To determine whether the sequence is arithmetic, geometric, or neither, we need to observe the pattern of the sequence.
In the given sequence 3, 6, 12, 24, ..., we can see that each term is obtained by multiplying the previous term by 2. Since there is a constant factor between each term, this sequence is a geometric sequence.
2. To write a function rule for the table, we need to find a pattern between the input (x) and the output (f(x)).
By comparing the values of x and f(x), we can see that f(x) is equal to the square of x. Therefore, the function rule is: f(x) = x^2 (x squared).
3. To write a rule to describe the function of the zucchini plant's height, we need to consider the initial height (12 centimeters) and the rate of growth (approximately 0.3 centimeters per day).
The rule for the height (H) in terms of the number of days (d) is: H(d) = 0.3d + 12.
4. To write a rule to describe the function of the sloth's travel, we need to consider the rate of travel (0.5 meters per minute).
The rule for the distance traveled (d) in terms of the time (t) is: d(t) = 0.5t.
In 8 minutes, the sloth will travel: d(8) = 0.5 * 8 = 4 meters.
5. Without providing the functions to choose from, it is not possible to determine which function is greatest at x = 2. Please provide the options for me to give a specific answer.
6. To calculate the total amount owed for the car loan, we need to consider the initial loan amount ($6,000), the annual interest rate (5%), and the loan duration (5 years).
The formula to calculate the total amount owed is: Total amount = Initial loan amount + (Initial loan amount * Interest rate * Loan duration) = $6,000 + ($6,000 * 0.05 * 5) = $6,000 + $1,500 = $7,500.
Therefore, the total amount your family owes for the car is $7,500.
7. To find the volume of water that will leak in 3 hours, we need to consider the leak rate (0.8 gallon per hour) and the number of hours (3).
The formula to calculate the volume of water (w) leaked in t hours is: w(t) = Leak rate * t = 0.8 * 3 = 2.4 gallons.
Therefore, the volume of water that will leak in 3 hours is 2.4 gallons.
8. To determine which of the given sequences is an arithmetic sequence, we need to observe the pattern between each term.
An arithmetic sequence has a constant difference between each term.
Looking at the options:
-1, 2, 5, 8, . . .: The difference between each term is 3, so this is an arithmetic sequence.
6, 9, 5, 8, 4, 7, . .: The difference between each term varies, so this is not an arithmetic sequence.
5, 20, 80, 320, . .: The difference between each term (5, 20, 80, ...) is not constant, so this is not an arithmetic sequence.
100, 10, 0.1, 0.01, . .: The difference between each term varies greatly, so this is not an arithmetic sequence.
Therefore, the arithmetic sequence is -1, 2, 5, 8, . . .
I don't see where you indicated your answer choices.
You didn't expect that somebody would just this test, assignment or homework for you , or did you ??
You would be totally amazed to find out that, after studying the topics, that
you can actually answer these questions all by yourself