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# hw1-25 - V t = 320 e-3 1 t where t is measured in seconds...

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Homework 1/25 1. A population of critters is measured by the function P ( t ) = 100(2 t/ 5 ) where t is measured in years and P is measured in critters. (a) Graph P ( t ) on the domain 0 t 15 years. Be sure to label your graph correctly. (b) Find P (0) (c) Find P (10) (d) Find the change in P on the interval 0 t 10 years. (e) Find Δ P on [0 , 10] (f) Find Δ P on [1 , 2] (g) When will the population be 500 critters? 2. The position of a moving object is measured by the function s ( t ) = 2 sin( π ( t - 0 . 5)) where t is measured in minutes and s is measured in feet. (a) Graph s ( t ) on the domain 0 t 4 minutes. Be sure to label your graph correctly. Also label all intercepts. (b) Find the change in position on the interval 0 t 1 minute. (c) Find Δ s on [0 . 5 , 1] (d) Find Δ s on [1 , 1 . 5] (e) When is the position 1 foot? List all times in the domain [0 , 4]. (f) When is the position - 2 feet? List all times in the domain [0 , 4]. 3. The voltage across a capacitor is given by

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Unformatted text preview: V ( t ) = 320 e-3 . 1 t where t is measured in seconds and V is measured in Volts. (a) Graph V ( t ) on the domain 0 ≤ t ≤ 3 seconds. Be sure to label your graph correctly. (b) Find V (0) (c) Find V (1) 1 (d) Find Δ V on [0 , 1] (e) Find Δ V on [0 , . 5] (f) Find Δ V on [0 , . 1] (g) When is the voltage 200 V? (h) Find an interval on which Δ V is-100 V. Hints and Answers 1. b) 100 critters; c) 400 critters; d) 300 critters; e) 100(2 2 / 5-2 1 / 5 ) ≈ 17 critters; f) 5 ln 5 / ln 2 ≈ 11 . 6 years. 2. b) 4 ft; c) 2 ft; d) -2 ft; e) 2/3, 4/3, 8/3 and 10/3 seconds; f) 0, 2 and 4 sec. 3. b) 320 V; c) 14.4 V; d)-306 V; e)-252 V; f)-85 . 3 V; g) 0.152 s h) Chose any convenient time for one end. Try to solve for the other end. 2...
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