1. [19 Points] DETAILS MY NOTES ASK YOUR TEACHER A population of rabbits is described by the function R(t) = 100(25'5), where t is measured in months and R is measured in rabbits. Create a clear and properly labeled graph of RU) on the domain El 5 t 5 15 months. Proper labeling includes at least: I A name on the input axis. This can be a variable or a word. - Units on the input axis. - Tlckmarks on the input axis, with enough ofthem numbered so that scale is apparent. - All of the above on the output axis. a. Which graph below correctly follows the instructions on the worksheet. 500 A g 600 2 a. 500 s t 5\" g 400 E 400 E B .1 300 E 300 3 200 E a: 200 100 100 2 4 6 3 10 12 2 4 6 8 10 12 O I? (Number of Rabbits) O 13 (months) .51. 600 9: E 500 E B L ._ E g 400 g a: E 300 3 z D: 200 100 2 4 6 8 10 12 O t (months) 0 Time Explain the flaw in each incorrect option. b. Find the change in R on the interval 0 5 1'5 10 months Jand select the correct units from 0 no units 0 rabbits/month O rabbits 0 months c. Find AR on [1,2]. Round your answer to the nearest whole numberS and select the correct units from O rabbits 0 months 0 no units 0 rabbitsr'month d. Find the average rate of change of R on the interval 5 5 ts 7 months. Your answer must be accurate to two decimal places. Select the correct units from 0 no units 0 rabbits O rabbits/month 0 months Then, in your original graph of Ra). sketch a secant line that corresponds to this rate of change. e. Find % on [25]. Your answer must be accurate to one decimal place. :] Select the correct units from O rabbits 0 rabbits/month 0 months 0 no units Then, in your original graph of Ra). sketch the corresponding secant line. NOTE: At the conclusion of this problem you should have a worksheet with a good graph of R(t) that includes two secant lines. Save this graph. You may be asked to turn it in later. 2. {13 Points] DETAILS MY NOTES ASK YOUR TEACHER The position of a moving object is given by 5(t) = 2.15in(7r(t70.2)), Where t is measured in minutes and sis measured in feet. Use your own paper (graph paper recommended, but not required) to create a clear and properly labeled graph of5(t) on the domain U s t s 4 minutes. After your graph is complete: 1. Find % on each of the intervals listed below. All answers must have two decimal places of accuracy and correct units. Sketch the corresponding secant lines in your original graph of 3(1). [1.3.2.0] [1.9.2.0] [2.0.2.1] NOTE: At the conclusion of this problem you should have a good graph of 5(t) that includes three secant lines. Save this graph. You may be asked to turn it in later. Submit Answer 3. {-14 Points] DETAILS MY NOTES ASK YOUR TEACHER The table below gives the height, h, of a falling object (in feet) at various times, t (in seconds). h(ft) 100 99 96 91 84 75 64 51 36 t(s) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Use your own paper (graph paper recommended, but not required) to create a clear and properly labeled graph of hm on the domain 0 5 t 5 2 seconds. After your graph is complete: 1. Find the average velocity of the object on each of the intervals listed below. All answers must be accurate to one decimal place. Sketch corresponding secant lines. [0.50.100] [0.15.100] [1.00.125] [1.00.1.50] Submit Answer 4. [14 Points] DETAILS MY NOTES ASK YOUR TEACHER The electric potential in a circuit is given by V(t) = 32091\5. [11 Points] DETAILS MY NOTES ASK YOUR TEACHER NOTE: This is your first matching question. You should select an option from each pull down menu before you click "submit". You only get 10 submissions on this problem. Click the (+) in the upper left of question to see how many submits you have. The figure below shows a function, x), and four secant lines labeled A, B, C and D. Each secant line corresponds to an average rate of change. Match the letters to the appropriate rate of change below. Put the letter E on the rate of change that does not correspond to any of the secant lines. Af - A on 2.2.4 V M [ ] Af _ A 2.3.6 " M on [ ] Average rate of change of f(x) on [0.4,2] - c Af _ A on 2,3 V Ax [ ] ion [1,2] ' C Ax Submit Answer 6. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER A stone is tossed in the air from ground level with an initial velocity of 25 m/s. Its height at time t is Mt) = 25f 4.9t2 m. Compute the stone's average velocity over the time interval [.5, 2.5]. Include units in your answer. Submit