11Brev2andahalf

# 11Brev2andahalf - -Y ) , where Y is the size of the bass...

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ucsc econ/ams 11b Review Questions 2.5 Table of integrals and separable diﬀerential equations 1. Compute the following integrals a. Z 5 x 7 - 2 xdx = b. Z 7 t 2 + 3 t - 1 2 + 5 t dt = c. Z 500 t 2 e - 0 . 04 t dt = d. Z 3 e 2 x 4 + e x dx = e. Z 300 1 + 0 . 25 e - 0 . 1 t dt = f. Z 4(ln x ) 2 3 x 2 + 7 ln x dx = 2. Let y = f ( x ) satisfy (i) dy dx = 3 xy 2 and (ii) y (1) = 2. Find the function f ( x ). 3. The income-elasticity of demand for a ﬁrm’s product is proportional to the square root of income. Find the demand as a function of income, given that q (100) = 50 and q (400) = 90. 4. The population of bass in a large lake grows according to the (logistic) model, dY dt = 0 . 05 Y (10
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Unformatted text preview: -Y ) , where Y is the size of the bass population, measured in 1000s of ﬁsh, and t is measured in years. (I.e., if the population is 2000, then Y = 2.) (a) If the bass population in 1990 was 1500, what will the population be in 2010? (b) When will/did the bass population reach 5000? (c) Once the population reaches 3000, bass are ‘harvested’ from the lake at the con-stant rate of 1000 ﬁsh per year. Describe what will happen to the ﬁsh population over time....
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## This note was uploaded on 03/15/2010 for the course ECON 11 taught by Professor Yk during the Spring '10 term at University of California, Santa Cruz.

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