PLZZZ HELP I NEED IT NOW!!!

1. Use the graph to write an explicit function to represent the data and determine how much money Taryn earned in week 5.

graph with x axis labeled Number of Weeks and ranges from zero to seven, y axis labeled Money Earned, in dollars, and ranges from zero to one hundred eighty with points at one comma four, two comma twelve, three comma thirty six, and four comma one hundred eight

f(n) = (3)n − 1; f(5) = 81

f(n) = 4(3)n + 1; f(5) = 2,916

f(n) = 4(3)n; f(5) = 972

f(n) = 4(3)n − 1; f(5) = 324

2. The annual growth of Noah's worm collection is represented by the table. What does f(x) = 4 represent?

x 0 2 4
f(x) 4 16 64

The number of new worms each year
The number of worms Noah started with
The common ratio of worm growth
The average rate of change of worm growth each year

3.
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

f(x) = 250(1.25)x

Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers

Question

05-10-2019
Mathematics

contestada

PLZZZ HELP I NEED IT NOW!!!

1. Use the graph to write an explicit function to represent the data and determine how much money Taryn earned in week 5.

graph with x axis labeled Number of Weeks and ranges from zero to seven, y axis labeled Money Earned, in dollars, and ranges from zero to one hundred eighty with points at one comma four, two comma twelve, three comma thirty six, and four comma one hundred eight

f(n) = (3)n − 1; f(5) = 81

f(n) = 4(3)n + 1; f(5) = 2,916

f(n) = 4(3)n; f(5) = 972

f(n) = 4(3)n − 1; f(5) = 324

2. The annual growth of Noah's worm collection is represented by the table. What does f(x) = 4 represent?

x 0 2 4
f(x) 4 16 64

The number of new worms each year
The number of worms Noah started with
The common ratio of worm growth
The average rate of change of worm growth each year

3.
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

f(x) = 250(1.25)x

Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers

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Ashraf82 Ashraf82 · Answer 1 · 2019-10-15T15:37:34+02:00

1. The explicit function that represents the data is

f(n) = [tex]4(3)^{n-1}[/tex] and Taryn earned 324 in week 5 ⇒ 4th answer

2. f(x) = 4 represents the common ratio of worm growth ⇒ 3rd answer

3. The reasonable domain for the function is 0 ≤ x ≤ 30 ⇒ 2nd answer

Step-by-step explanation:

1.

The graph passes through points (1 , 4) , (2 , 12) , (3 , 36) , (4 , 108)

∵ 12 ÷ 4 = 3 , 36 ÷ 12 = 3 , 108 ÷ 36 = 3

There is a constant ratio between the y-coordinates of the points on

the graph

∴ The graph represents an exponential function with a growth factor 3

The general form of the exponential function is f(x) = [tex]a(b)^{x}[/tex],

where a is the initial value and b is the growth factor

∵ x-axis represents the number of weeks n

∵ y-axis represents the money earned

∵ The factor of growth b = 3

∵ The points started from n = 1 not zero and initial value found

when the exponent = 0

∴ The exponent must be n - 1

∴ f(n) = [tex]a(3)^{n-1}[/tex]

Substitute the first point in the function to find the value of a

∵ n = 1 and f(n) = 4

∴ 4 = [tex]a(3)^{1-1}[/tex] = [tex]a(3)^{0}[/tex]

∵ [tex]3^{0}=1[/tex]

∴ a = 4

∴ f(n) = [tex]4(3)^{n-1}[/tex]

∵ n = 5

∴ f(5) = [tex]4(3)^{5-1}[/tex] = [tex]4(3)^{4}[/tex] = 4 × 81

∴ f(5) = 324

The explicit function that represents the data is f(n) = [tex]4(3)^{n-1}[/tex]

and Taryn earned 324 in week 5

2.

The annual growth of Noah's worm collection is represented by

the table:

x : 0 2 4

f(x) : 4 16 64

∵ 16 ÷ 4 = 4 , 64 ÷ 16 = 4

There is a constant ratio 4 between each two consecutive values of f(x)

∴ The growth factor of the exponential function is 4

∴ f(x) = 4 represents the common ratio of worm growth

f(x) = 4 represents the common ratio of worm growth

3.

f(x) = [tex]250(1.25)^{x}[/tex], where

250 represent the initial value of population

1.25 is the factor of growth

∵ The function represents the population of the bird in month

September

∵ September is 30 days

∴ The reasonable domain for the function is 0 ≤ x ≤ 30

When x = 0 the population of bird is 250 ⇒ initial value

When x = 30 the population of the bird is 201948 ⇒ final value

The reasonable domain for the function is 0 ≤ x ≤ 30

Learn more:

You can learn more about the exponential function in

brainly.com/question/2510325

#LearnwithBrainly

joyjoyduke joyjoyduke · Answer 2 · 2022-01-13T14:28:14+01:00

joyjoyduke joyjoyduke

13-01-2022

Answer:

(d) , f(n) = 4(3)n − 1; f(5) = 324

Step-by-step explanation:

i took the test

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