Exam 1: A Library of Functions

Draw a graph which accurately represents the temperature of the contents of a cup left overnight in a room.Assume the room is at 70° and the cup is originally filled with water slightly above the freezing point.

Cramped Quarters Island is a tiny island which, although able to support a limited population of rabbits, doesn't have enough space or food supplies to support unlimited exponential growth.It is suggested that if Q(t)= population of rabbits on Cramped Quarters Island at time t, then the quantity (800 - Q(t))will be an exponentially decaying function of t.If at time t = 0 there were 250 rabbits, and the population was increasing at an instantaneous rate of 100 rabbits per year, give the general formula for $Q(t)$ .

What is the period of the function $g(t)=9+8 \cos \pi t$

The solid curve below is a portion of the graph of $f(x)=8 x^{3}$ and the dashed curve is a portion of the graph of $g(x)=e^{0.25 x}$ .The domain of both functions is all real numbers.Which of the following statements are true.Check all that apply.

A function is linear for x $\le$ 2 and also linear for x $\ge$ 2.This function has the following values: f(-4)= 8; f(2)= 5; f(4)= 11.Find formula(s)(or equation(s))which describe this function.

Using base e and transformations, find a formula for the exponential function shown in the graph below.

Given the function $f(x)=e^{-x^{2} / 3}$ find $g(x)$ and $h(x)$ such that $f(x)=g(h(x))$

The following table defines three functions for $0 \leq x \leq 4$ .The function $y_{1}$ is most likely x 0 4.65 4.65 4.65 1 7.44 5.11 3.79 2 11.90 5.97 2.93 3 19.05 9.55 2.07 4 30.47 15.28 1.21

A bakery has 300 lbs of flour.If they use 10% of the available flour each day, how much do they have after 20 days? Round to the nearest pound.

Cramped Quarters Island is a tiny island which, although able to support a limited population of rabbits, doesn't have enough space or food supplies to support unlimited exponential growth.It is suggested that if Q(t)= population of rabbits on Cramped Quarters Island at time t, then the quantity (800 - Q(t))will be an exponentially decaying function of t.Given that there were 400 rabbits at time t = 0, and 500 rabbits one year later, find the general formula for Q(t), the population of rabbits on Cramped Quarters Island at time t and use it to determine the rabbit population after 3 years (to the nearest rabbit).

You have $500 invested in a bank account earning 6.4% compounded monthly, earning $\frac{6.4}{12} \%$ interest each month.How much interest do you earn the first year? Round to the nearest cent.

A school library opened in January of 1980.In January, 2000 they had 35,000 books.One year later, they had 35,490 books.Assuming they acquire the same number of books at the start of each month, how many books did they have in July of 1980?

The following describes a function that must be invertible: N(p)is the number of words on page p of a science fiction novel.

What is the doubling time in years of prices which are increasing by 8% a year? Round to two decimal places.

If $f(x)$ and $g(x)$ are both continuous functions, what can you say about $f(x) / 8$ ?

You are offered two jobs starting on July 1^st of 2008.Firm A offers you $50,000 a year to start and you can expect an annual raise of 4% every July 1^st.At firm B you would start at $40,000 but can expect an annual 6% increase every July 1^st.After how many years would the job at firm B first pay more than the job at firm A?

Sketch a well-labeled graph of a periodic function such that : -- f(0)= 850 -- the period is 12 -- the amplitude is 550. Then write a few sentences illustrating how such a function might apply to a scorpion population.

At the point $x=-\pi$ , the function $c(x)=\cos 2 x+0.4 \cos 5 x$ has

Make a graphical sketch of the following function.Include a scale on the x- and y-axis. $y=4+3 \sin 2 x$

One of the functions below is a quadratic, one is a cubic, and one is a periodic function.Which one is periodic? x f(x) 0.2 -0.42 0.4 -0.65 0.6 0.96 0.8 -0.15 1.2 0.84 x g(x) 1.3 0.41 1.7 0.81 2.5 0.65 3.0 -0.10 3.5 -1.35 x h(x) 0.5 -1.13 1.2 0.13 1.8 0.03 2.0 0.00 2.2 0.05