Posted: November 13th, 2015

# Pre-Calculus

Pre-Calculus

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

in 1975.
p(t) =
(b) Give a linear model relating the price q of the Kamaka uke to the year t. Again

take 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?
t = 0
t = 0
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
tapes
3. –/12 pointsUWAPreCalc1 14.P.005.
Find the linear-to-linear function whose graph passes through the points and
f(x) =
What is its horizontal asymptote?
y =
4. –/12 pointsUWAPreCalc1 14.P.006.
Find the linear-to-linear function whose graph has as a horizontal asymptote and

passes through
f(x) =
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)
from the light source is given by where k is a constant depending on the light

source.
(1, 1), (4, 2) (30, 3).
y = 6
(0, 10) and (2, 8).
C = , k
d2
(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
t =
s