This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1.
a. Which of the following functions is represented by the graph sketched below? b. Find the derivatives of each of the followng functions: i) e3" ii) exlx iii) log5(x'2+X—7) 3g; “Zn/g)
3 9“ yew g W24 7;, c. Find the indeﬁnite integrals of each of the following functions: 2 K i) 63" 8.39.0?) we" ﬂew a}, I: ’5’ fﬁfiﬁw}; gay/)4 H39 [X el'XM‘ i 2. Consider the following function: f ( x ): 3+1
x +3 21. Find a domain where f (x) is invertible. b. If the inverse of f on this domain is g, what is the domain of g? . . . 10
c. Find the derivative g1?) .‘ 5’7) U #ﬁﬂﬁmf Mia/f ﬁr" Wei/I }A/§Wa§ s; _ r " w i a / j MW 62% w .37 . a? ,péWa w m (1.. 5, (if; «F 3. A biology lab experiment goes wrong, and a new organism gets loose.
It eats everything and starts growing exponentially. The technicians observe
that it went from a 1 liter volume to a volume of 4 liters in ten minutes At . that point they immediately evacuate the lab, leaving the organism at ters
to continue to grow. The lab is fairly large, with a volume of 300,000 liters.
[Note: this room is lots bigger than that] The standard exponential model for the volume in this situation, as we
know, is V(t)=V0ekt , where we will measure the time t in minutes from when the volume was measured at 1 liter, 10 minutes before the lab was
evacuated. a. What is V0 ?
b. What is the value of V( 10)? c. Find k. d. What is the doubling time for this monster? e. How long will it take to ﬁll the room? 4. A student has to borrow $5000 for tuition. After looking around, she
decides on a 5% loan. Payments will only start after graduation. a. If the interest is compounded once a year, how much will she owe when
she graduates in 4 years? ' 1). Her friend also gets a loan for $5000 at 5%, but the interest is
compounded continuously, and again no payments until graduation in 4
years. How much will he owe when he graduates? c. What is the present value of a graduation present of $5500 promised in
four years? age? (may)? 9 W}; ij "r a 5 5. Newton's Law of Cooling: y'=—k(y~T0) where k is the cooling constant,
and To is the ambient temperature. Suppose an object is dropped into a large body of water at 15° C. Suppose the object is initially at 3000 C. If the temperature cools down to 2000 C in
one hour,’ a. What is k? b. When will the object cool to 100° C? c. When will the temperature reach 15° C? ...
View
Full
Document
This note was uploaded on 04/06/2012 for the course MATH 31B taught by Professor Valdimarsson during the Fall '08 term at UCLA.
 Fall '08
 VALDIMARSSON
 Math

Click to edit the document details