Pre-Calculus
1. –/10 pointsUWAPreCalc1 14.P.003.
In 1975, I bought an old Martin ukulele for $300. In 1995, a similar uke was selling for $1200. In 1980,
I bought a new Kamaka uke for $75. In 1990, I sold it for $325.
(a) Give a linear model relating the price p of the Martin uke to the year t. Take t = 0 in 1975.
p(t) =
(b) Give a linear model relating the price q of the Kamaka uke to the year t. Again take t = 0 in
1975.
q(t) =
(c) In what year is the value of the Martin twice the value of the Kamaka?
(d) Give a function f(t) which gives the ratio of the price of the Martin to the price of the
Kamaka.
f(t) =
(e) In the long run, what will be the ratio of the prices of the Martin ukulele to the Kamaka
ukulele?
Additional Materials
Reading
2. –/12 pointsUWAPreCalc1 14.P.004.
Isobel is producing and selling cassette tapes of her rock band. When she had sold 10 tapes, her net
profit was $4. When she had sold 20 tapes, however, her net profit had shrunk to $2 due to increased
production expenses. But when she had sold 30 tapes, her net profit had rebounded to $10.
(a) Give a quadratic model relating Isobel’s net profit y to the number of tapes sold x.
y=
(b) Divide the profit function in part (a) by the number of tapes sold x to get a model relating
average profit w per tape to the number of tapes sold.
w=
(c) How many tapes must she sell in order to make $2.03 per tape in net profit? (Enter your
answers as a comma-separated list. Round your answers to the nearest whole number.)
tapes
Additional Materials
Reading
3. –/12 pointsUWAPreCalc1 14.P.005.
Find the linear-to-linear function whose graph passes through the points (1, 1), (4, 2) and (30, 3).
f(x) =
What is its horizontal asymptote?
y=
Additional Materials
Reading
4. –/12 pointsUWAPreCalc1 14.P.006.
Find the linear-to-linear function whose graph has y = 6 as a horizontal asymptote and passes through
(0, 10) and (2, 8).
f(x) =
Additional Materials
Reading
5. –/12 pointsUWAPreCalc1 14.P.008.
A street light is 9 feet above a straight bike path. Olav is bicycling down the path at a rate of 15 MPH. At
midnight, Olav is 33 feet from the point on the bike path directly below the street light. (See the
picture.) The relationship between the intensity C of light (in candlepower) and the distance d (in feet)
k
from the light source is given by C = 2 , where k is a constant depending on the light source.
d
(a) From 21 feet away, the street light has an intensity of 1 candle. What is k?
k=
(b) Find a function which gives the intensity I of the light shining on Olav as a function of time t,
in seconds.
I(t) =
(c) When will the light on Olav have maximum intensity? (Round your answer to one decimal
place.)
t=
s
(d) When will the intensity of the light be 2 candles? (Enter your answers as a comma-separated
list. Round your answers to two decimal places.)
t=
s
Additional Materials
Reading