2. The temperature of a potato placed in a preheated oven
is given by
where P is degrees Fahrenheit and t is minutes since the
potato was placed in the oven.
(a) Graph P as a function of t for values of t up to 120 minutes.
(b) The potato is cooked when it reaches 270 degrees. When will the potato be
(c) What is the initial temperature of the potato?
(d) Did the potato’s temperature rise more in the first thirty minutes or the
(e) What is the concavity of the graph of P (concave up or concave down) ?
what this means in terms of the temperature of the potato.
(f) Sketch a graph of dP/dt as a function of t.
(g) Explain how your graph in (f) is related to the concavity of the graph of P.
(h) Let Q = P − 400.
3. A local band has made a music CD which they are
selling. The manager has told you that
they make the same profit for each CD sold. The profit is the revenue from CD
the fixed costs for the studio and equipment rental. The manager has carefully
the amount of profit for various numbers of CD sold:
Numbers of CDs sold
(a) Explain why the profit is a linear function of the
number of CDs sold.
(b) Calculate the slope of the linear function of Part (a).
(c) What is the meaning of the slope in terms of CD sales?
(d) Calculate the vertical intercept of the linear function of Part (a).
(e) What is the meaning of the vertical intercept in terms of CD sales?
(f) Calculate the horizontal intercept of the linear function of Part (a).
(g) What is the meaning of the horizontal intercept in terms of CD sales?
(h) Suppose your estimates for possible sales indicate that you will only sell
How much should you charge to ensure that your fixed costs will be covered by
4. The fol lowing table shows U.S. population from census
Population (in millions)
(a) On this paper plot the logarithm of the population as
a function of t, years since
(b) What property of the plot from (a) allows you to conclude that the original
(c) Find an exponential function which best approximates the population as a
(d) What is the annual percentage growth rate of the population?
(e) What is the decade percentage growth rate of the population?
(f) Estimate the population in 1870. The actual figure was about 39 million.
could explain the difference between your exponential model prediction and the
(g) The decade growth rate from 1930 to 1940 was 7.2%. Is that very high, high,
right, low, or very low in comparison with what you’d expect based on the data
1800 to 1840?
5. A jug of water is being drained by holding a spigot
open. Here is depth of water W in
inches at various t, minutes that the spigot has been open:
Time open t
Water depth W
(a) Show that W can be modeled as a quadratic function of
(b) Write a formula for W as a quadratic function of t.
(c) How long will it take for the jug to be completely drained?
(d) Is W increasing or decreasing?
(e) Is positive or negative ?
(f) Explain why is linear.
(g) Carefully make three graphs:
i. Graph W as a function of t for t from zero until the jug is drained.
ii. Sketch a graph of as a function of t for
the same interval.
iii. Sketch a graph of the rate of change of ,
that is, the second order rate of
change of W, as a function of t for the same interval.
6. For each of the following data tables determine whether
the data is linear, quadratic,
exponential, or power and give the appropriate formula. For credit you must
Start solving your Algebra Problems
in next 5 minutes!
Download (and optional CD)
Click to Buy Now:
2Checkout.com is an authorized reseller
of goods provided by Sofmath
Attention: We are
currently running a special promotional offer
for Algebra-Answer.com visitors -- if you order
Algebra Helper by midnight of
you will pay only $39.99
instead of our regular price of $74.99 -- this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
If you order now you will also receive 30 minute live session from tutor.com for a 1$!
You Will Learn Algebra Better - Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)