Modeling With Functions

Maria is making a rectangular garden. The length of the garden is 2 yards greater than its width, w, in yards.

Enter the function, f(w), that describes the area, in square yards, of Maria’s garden as a function of the width, w.

• f(w) = w(2w)

• f(w) = w(w + 2)

• f(w) = l(w + 2)

• f(w) = w²

Barb traveled 300 miles during the first 5 hours of her trip. Barb then traveled at a constant speed of 50 miles per hour for the remainder of the trip.

Write the function, f(t), that describes the average speed during the entire trip as a function of time, t, in hours, Barb traveled after her first 300 miles.

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A washing machine was purchased for $256.

Each year the value is ¼ of its value the previous year.

Enter the function, f(t), that describes the value of the washing machine, in dollars, as a function of time in years, t, after the initial purchase.

• f(t) = 256(0.75)^t

• f(t) = 256(0.25)^t

• f(t) = 256(1.25)^t

• f(t) = 256(1.75)^t

A researcher studies the growth of a fruit fly population. The researcher counts the number of fruit flies at noon each day. The results are in the table.

• V(n) = Total number of fruit flies after n days

• V(0) = 4

Enter the function for n ≥ 1, which describes the number of fruit flies, V(n), at noon on the n^th day in terms of the number of fruit flies at noon on the previous day, V(n − 1).

• V(n) = V(n – 1) + 2

• V(n) = 4V(n – 1)

• V(n) = 2V(n – 1)

• V(n) = V(n – 1) + 1

The first row in a theater has 8 seats, the second row has 11 seats, the third row has 14 seats and the fourth row has 17 seats. The pattern of increasing each successive row by 3 seats continues throughout the theater.

• f(r) = the number of seats in row r

• f(1) = 8

Write an equation, for r ≥ 2, which describes the number of seats, f(r), in the r^th row in terms of the number of seats in the (r − 1)^th row, f(r − 1).

• f(r) = f(r − 1) + 3

• f(r) = f(r − 1) + 8

• f(r) = 3f(r − 1)

• f(r) = 8f(r − 1)

The 13th row in a theater has 41 seats, the

12th row has 38 seats, the 11th row has 35 seats and the 10th row has 32 seats. The pattern of decreasing each successive row by 3 seats continues from the 13th row to the 1st row.

• f(r) = the number of seats in row r.

• f(1) = 5

Enter an equation, for r ≥ 2, that describes the number of seats, f(r), in the r^th row in terms of the number of seats in the (r − 1)^th row, f(r − 1). Assume that the pattern described applies to all rows.

• f(r) = f(r − 1) - 3

• f(r) = f(r − 1) + 5

• f(r) = f(r − 1) + 3

• f(r) = f(r − 1) + 13

Consider this function in explicit form:

f(n) = 3n − 4; n ≥ 1

Select the equivalent recursively defined function.

• f(1) = −1

  f(n) = f(n − 1) + 3; n ≥ 2

• f(1) = −1

  f(n) = 3f(n − 1); n ≥ 2

• f(0) = −4

  f(n) = 3f(n − 1); n ≥ 2

• f(0) = −4

  f(n) = f(n − 1) + 3; n ≥ 2

Consider this function in recursive form.

f(1) = −3

f(n) = 3f(n − 1); n ≥ 2

Select the equivalent explicit function for n ≥ 1.

• f(n) = −3(n)

• f(n) = −3(n − 1)

• f(n) = −3(3)ⁿ

• f(n) = −3(3)⁽ⁿ⁻¹⁾

The functions in the table are defined for integers n ≥ 1. Match the recursively defined function with the equivalent

explicit form.

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The functions in the table are defined for integers n ≥ 1. Match the recursively defined function with the equivalent

explicit form.

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