Introduction to Modeling with Functions

Question 1

Sophia plots points on a graph to represent the shape of a concave lens.

Revolt · Accepted Answer

quadratic

Question 2

Cherie measures and records the lengths and sizes of the same style of a sandal found at a shoe store.

Revolt · Accepted Answer

S = 2x – 10

Question 3

The graph shows the relationship between the amount of change given from a $10 bill and the number of bagels purchased.

Revolt · Accepted Answer

f(x) = + 10

Question 4

A graph is drawn to represent a relationship between distance, d, and time, t.

Revolt · Accepted Answer

Each point shows the remaining distance, in feet, to the finish line of a race t seconds after a runner begins the final stretch and runs at a constant speed.

Question 5

The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

Revolt · Accepted Answer

y = 50(0.85)t

Question 6

Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the noodles, in centimeters, needed for the arch to increase the length of the bridge in 1-centimeter increments.

Revolt · Accepted Answer

f(x) = –0.5(x – 5)2 + 8

Question 7

The graph shows the population of a bacteria in an experiment, measured every hour.

Revolt · Accepted Answer

f(t) = 10(1.4)t

Question 8

The graph shows the daily revenue earned selling coupon cards in a fundraiser if the price is decreased by x dollars.

Revolt · Accepted Answer

R(x) = –x2 + 6x + 40

Question 9

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Revolt · Accepted Answer

; 13.5 mg

Question 10

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.Which graph could represent the area of each rectangle in terms of the change in the length and width?

Revolt · Accepted Answer

A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.

Introduction to Modeling with Functions Answers

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