UCLA Fall 2011 Math 31B midterm solution

# UCLA Fall 2011 Math 31B midterm solution - 1. a. Which of...

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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? ...
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## This note was uploaded on 04/06/2012 for the course MATH 31B taught by Professor Valdimarsson during the Fall '08 term at UCLA.

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UCLA Fall 2011 Math 31B midterm solution - 1. a. Which of...

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