An object is launched straight upward so that its height, h, is a function of time, t, with

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1 WebAssign Lesson 13-3 Applications (Homework) Current Score : / 18 Due : Wednesday, April :00 AM MDT Shari Dorsey Sp 14 Math 170, section 003, Spring 2014 Instructor: Shari Dorsey 1. /1 points The potential in a circuit, V, is a function of time, t, with V(0) = 0 volts, and dv = 18e 1.5t volts/sec. Find V(0.5). Be accurate to 2 decimal places. V(0.5) = 2. /1 points h(0) = 100 feet, and = t feet/second. Find Δh on the interval 0 t 2 seconds. Be accurate to 1 decimal place. Δh = 3. /2 points An object moves up and down. Its position, y, is a function of time, t, with y(0) = 2.25 m, and dy = 1.5 sin(2t) m/s. Write an algebraic formula for y. Your answer will have t in it. Your answer should not have an integral in it. y(t) = Write a formula for Δy on the interval [0, t]. Your answer will have t in it. Your answer should not have an integral in it. Δy =

2 4. /2 points h(0) = 100 feet, and = t feet/second. Find when h(t) = 0. Assume t > 0. Be accurate to 3 decimal places. t = At that instant, how fast is it moving? (Just as it hits, so not 0.) Be accurate to 2 decimal places.

3 5. /3 points A projectile is launched straight up. Its height is a function of time, h(t). Its velocity is graphed below. Answer the following questions. Give exact answers with correct units. What is Δh on the interval 0 t 3 seconds? Compute the integral: If Δh on [0, b] is 20 m, what is b? (There are two possible answers. Find the smaller one.) Δh = 5 h'(t) = 2 b = 6. /1 points The price of a certain commodity is expected to change at a rate of 15 P'(t) = $/lb/day (0.5t+1) 2 How much will the price change during the next week? Round your answer to the nearest penny/lb.

4 7. /1 points Water flows into an empty reservoir at a rate of t liters per hour. What is the quantity of water in the reservoir after 5 hours? Click here for help on unit abbreviations. 8. /1 points h(0) = 5 m, and = t m/s. Find the maximum height. Be accurate to 3 decimal places. 9. /2 points An object is launched straight upward so that its height, h, is a function of time, t. h(0) = 0 feet, = v t feet/second, where v 0 is an unknown constant, and the object hits the ground when t = 5 seconds. Find v 0, accurate to 1 decimal place with correct units. v 0 = Find the maximum height. Be accurate to 3 decimal places, with units. 10. /1 points An object is cooling off. The rate of change of its temperature, T, is dt = 20e ct K/min. Here T is in Kelvins (K), t is in minutes, and c is an unknown constant. On the time interval 0 t 20 minutes the total change in temperature is ΔT = 150 K. Find c, accurate to 3 decimal places with correct units. c =

5 11. /1 points An object moves up and down so that its height, h, is a function of time, t. Height is in cm, time is in seconds, and velocity is = sin(8.2t) cm/s If h(0) = 2 cm, what is the maximum height the object can attain? Be accurate to 1 decimal place and include correct units. 12. /2 points A population of critters grows according to a logistic population model, p(t), with p(0) = 1000 critters, and dp = 500e 0.25t (1+e 0.25t ) 2 critters/year. Find p(10). Round your answer to the nearest critter. You don't need to include units. p(10) = critters When will there be 1500 critters? Be accurate to 2 decimal places. Include units. t =