Radical Word Problems

Mrs. Slate, a math teacher, is a huge Post Malone fan. She notices that the number of Post's Instagram followers over time can be modeled by the function f(x) = sqrt(2x), where x is the number of months since January 2023. In which month will Post's follower count reach 28 million?

• Month 392

• Month 64

• Month 28

• Month 16

Answer explanation

To find when Post's followers reach 28 million, set f(x) = sqrt(2x) = 28. Squaring both sides gives 2x = 784, so x = 392. Thus, it will take 392 months since January 2023.

Tags

CCSS.8.EE.A.2

Mrs. Slate is organizing a Post Malone concert at her school. The stage design includes a backdrop shaped like a radical function. The original function is f(x) = sqrt(x). If Mrs. Slate wants to stretch the design horizontally by a factor of 2 and reflect it over the x-axis, what is the new function that represents the transformed backdrop?

• f(x) = sqrt(2x)

• f(x) = -sqrt(2x)

• f(x) = -sqrt(x/2)

• f(x) = (1/2)sqrt(-x)

Answer explanation

To stretch horizontally by a factor of 2, replace x with x/2. Reflecting over the x-axis changes the sign. Thus, f(x) = -sqrt(x/2) is the transformed function, making it the correct choice.

Tags

CCSS.HSF.BF.B.3

Post Malone's tattoo artist charges according to the function C(x) = 100sqrt(x), where x is the number of hours spent on a tattoo and C(x) is the cost in dollars. If Post Malone has budgeted $500 for his next tattoo, how many hours can the tattoo artist spend on it?

• 4 hours

• 9 hours

• 25 hours

• 49 hours

Answer explanation

To find the hours, set C(x) = 500: 100sqrt(x) = 500. Dividing by 100 gives sqrt(x) = 5. Squaring both sides results in x = 25. Thus, the tattoo artist can spend 25 hours.

Tags

CCSS.HSA.REI.A.2

Mrs. Slate and Post Malone are collaborating on a math-themed music video. They want to incorporate a radical function that starts at the origin, passes through the point (4, 2), and opens upward. Find a function of the form f(x) = a(sqrt(x)) that satisfies these conditions.

• f(x) = (1/2)sqrt(x)

• f(x) = 2sqrt(x)

• f(x) = sqrt(x)

• f(x) = (1/4)sqrt(x)

Answer explanation

To find the function f(x) = a(sqrt(x)), we use the point (4, 2). Plugging in, we get 2 = a(sqrt(4)) => 2 = 2a => a = 1. Thus, f(x) = sqrt(x) satisfies all conditions, including starting at the origin and passing through (4, 2).

Tags

CCSS.HSF-IF.C.7B

Tags

A.NR.5.2

Mrs. Slate is creating a math puzzle for her students using Post Malone's album sales data. The sales are modeled by the function s(x) = sqrt(3x), where x is the number of weeks since the album's release. If the sales reach 15,000 albums, how many weeks have passed since the release?

• Week 25

• Week 75

• Week 5

• Week 45

Tags

CCSS.HSA.REI.A.2

Post Malone's new merchandise line is modeled by the function m(x) = sqrt(x) + 5, where x is the number of days since the launch and m(x) is the number of items sold in hundreds. If he wants to adjust the model to reflect a decrease of 3 items sold per day, what is the new function?

• m(x) = sqrt(x) + 2

• m(x) = sqrt(x) - 3

• m(x) = sqrt(x) + 8

• m(x) = sqrt(x) - 5

Ethan, Harper, and Abigail are planning to plant flowers in a rectangular garden. The garden has a length of √18 meters and a width of √12 meters. Calculate the area of the garden where they can plant the flowers?

• 6√6

Tags

CCSS.HSN.RN.A.2

Luna, Benjamin, and Isla are playing in a square field that has a side length of √32 meters. They want to race around the perimeter of the field. How long is the race track?

Tags

CCSS.7.EE.B.3

Scarlett, Daniel, and Ethan are on a treasure hunt and they stumble upon a mysterious rectangular prism. The prism has dimensions of √7 meters, √15 meters, and 2√3 meters. Evaluate the volume of this prism? Volume = length x width x height

Tags

CCSS.7.EE.B.3