MATH SOLVE

3 months ago

Q:
# 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 eightf(n) = (3)n − 1; f(5) = 81f(n) = 4(3)n + 1; f(5) = 2,916f(n) = 4(3)n; f(5) = 972f(n) = 4(3)n − 1; f(5) = 3242. The annual growth of Noah's worm collection is represented by the table. What does f(x) = 4 represent?x 0 2 4f(x) 4 16 64The number of new worms each yearThe number of worms Noah started withThe common ratio of worm growthThe average rate of change of worm growth each year3. 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)xWhich of the following is a reasonable domain for the function?0 ≤ x ≤ 2500 ≤ x ≤ 30All positive integers greater than 100All real numbers

Accepted Solution

A:

1. The explicit function that represents the data isf(n) = [tex]4(3)^{n-1}[/tex] and Taryn earned 324 in week 5 ⇒ 4th answer2. f(x) = 4 represents the common ratio of worm growth ⇒ 3rd answer3. 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 = 3There is a constant ratio between the y-coordinates of the points onthe graph∴ The graph represents an exponential function with a growth factor 3The 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) = 324The explicit function that represents the data is f(n) = [tex]4(3)^{n-1}[/tex] and Taryn earned 324 in week 52.The annual growth of Noah's worm collection is represented by the table:x : 0 2 4f(x) : 4 16 64∵ 16 ÷ 4 = 4 , 64 ÷ 16 = 4There 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 growthf(x) = 4 represents the common ratio of worm growth3.f(x) = [tex]250(1.25)^{x}[/tex], where250 represent the initial value of population1.25 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 ≤ 30When x = 0 the population of bird is 250 ⇒ initial valueWhen x = 30 the population of the bird is 201948 ⇒ final valueThe reasonable domain for the function is 0 ≤ x ≤ 30Learn more:You can learn more about the exponential function inbrainly.com/question/2510325#LearnwithBrainly