Posted: November 13th, 2015
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
(b) Give a linear model relating the price q of the Kamaka uke to the year t. Again
(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
(e) In the long run, what will be the ratio of the prices of the Martin ukulele to
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
(a) Give a quadratic model relating Isobel’s net profit y to the number of tapes
(b) Divide the profit function in part (a) by the number of tapes sold x to get a
average profit w per tape to the number of tapes sold.
(c) How many tapes must she sell in order to make $2.03 per tape in net profit?
answers as a comma-separated list. Round your answers to the nearest whole number.)
3. –/12 pointsUWAPreCalc1 14.P.005.
Find the linear-to-linear function whose graph passes through the points and
What is its horizontal asymptote?
4. –/12 pointsUWAPreCalc1 14.P.006.
Find the linear-to-linear function whose graph has as a horizontal asymptote and
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
(1, 1), (4, 2) (30, 3).
y = 6
(0, 10) and (2, 8).
C = , k
(a) From 21 feet away, the street light has an intensity of 1 candle. What is k?
(b) Find a function which gives the intensity I of the light shining on Olav as a
function of time t,
(c) When will the light on Olav have maximum intensity? (Round your answer to one
t = s
(d) When will the intensity of the light be 2 candles? (Enter your answers as a
list. Round your answers to two decimal places.)
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