Modeling With Functions

Compare the rates of change. Which statement is true about functions A and B?

• They have the same rate of change

• A has a greater rate of change than B

• A and B both have negative rates of change

• A has a negative ROC and B has a positive ROC

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Write an equation for this situation.

• y=9.75x

• y=19x

• y=19.25x

• y=9.5x

Tags

CCSS.6.EE.C.9

Select the correct answer. The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3 inches more than the time, t. What will the volume, V, of the balloon be at t = 3 seconds?

• 36π cubic inches

• 72π cubic inches

• 288π cubic inches

• 972π cubic inches

Select the correct answer. The total daily cost (in dollars) of manufacturing scented candles is given by the function C(b) = 250 + 3b, where b is the number of candles manufactured. Which function represents the average manufacturing cost, A, in terms of b?

• A(b) = 250/b + 3b

• A(b) = 250/b + 3

• A(b) = (250 + 3b) × (b)

• A(b) = 250 + 4b

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Select the correct answer. The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t² - 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?

• 80h² + 100h + 690

• 80h² + 100h + 270

• 40h² + 140h + 570

• 40h² - 140h + 603

Tags

CCSS.HSF-BF.A.1C

Select the correct answer from each drop-down menu. Jack is playing a game. When a player wins 3 consecutive games, the player receives 10 bonus points and then the player’s total score, s, increases by 5% of the player’s current points. Jack currently has p points and has won 3 consecutive games. The function that represents a player’s points including the bonus points, b, is b(p) =

• 10

• p - 10

• p

• p + 10

Tags

CCSS.HSF.LE.B.5

Jack’s total score after winning the bonus points, given by the function (s ∘ b)(p), is

• 05p + 9.5

• 05p + 10.5

• 5p - 9.5

• 5p + 10.5

Tags

CCSS.HSF-BF.A.1C

Select the correct answer from each drop-down menu. Ashton works as a marketing manager for a consumer products firm. His total earnings, A, in x months is given by the function A(x) = 2,400x + 40x². His total savings, S, in x months is given by the function S(x) = 250x + 500. The function E(x) = 40x² + 2,150x - 500 represents Ashton’s total expenses in x months.

• 40x² + 2,650x + 500

• 40x² + 2,150x + 500

• 40x² + 2,150x + 500

• 40x² + 2,650x - 500

You take out a student loan for $80,000 with 2.75% annual interest to pay for your first year of college. This loan will cover all course fees and books. Which is the exponential growth equation to model this situation?

Tags

CCSS.HSF.LE.A.2