6/10/22. 21:53 AM Dam-rm of Exponential and Logarithmic \"Inch-nus um Amman Listen out of 48 Derivatives of Exponential and Logarithmic Functions Unit Assignment You may choose to complete your mathematical calculations by hand and scan or take images to upload to the dropbox. To help your teacher review your work, please try to submit your calculations as a single file document (preferably as a pdf). If you aren't sure how to do this, please contact your teacher for assistance. Important When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: 0 Provide full solutions, showing all of your steps. 0 Make sure that there is one step or idea per line. 0 Use one equal sign per line. 0 Make sure that equal signs line up vertically. o Don't use self-developed short form notations. Note that derivatives must be fully simplied for full marks on this assignment. 1. Find the derivatives of each of these functions: (2 marks each) a. y : 1n(4z2 + 4) hllpsd/lmswimnlhiysnhwlcnm/le/ldenhmsquViewu/mmhhttps%3A%7F%2F737Sed>lee-AELMI-daBJeclWSLseqncnmeibghtspmem. 1/2 6/10/22, 21:53 AM Dam-Am of Exponential and Logarithmic Hmorinns um Amman 21' b.y=e7 c. y = 25+7(1n(52 + 1)) 4x\" 251\"" d.y= 2. Use the process of implicit differentiation to find a\" given that 2%\" 7 ya\" = 0. (4 marks) 3. Use curve sketching methods, sketch the graph of the function given by the equation y : jj. Make sure that you include all steps, charts, and derivations details. (10 marks) 4. Use logarithmic differentiation to find the derivative of the function 3 A = W16 marks) 5. The population, P, of an island, y years after colonization is given by the function P = %. a. What was the initial population of the island? (2 marks) b. How long did it take before the island had a population of 150? (2 marks) c. After how many years was the population growing the fastest? (3 marks) d. Using curve sketching methods, sketch the graph of the function. Make sure that you include all steps, charts, and derivations details. (10 marks) e. Give a possible explanation for the shape of the curve. (3 marks) Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will contribute to your overall final grade in this course, hnpsd/lmLi/imnlhiysnhoolcum/le/ldenhanmdseqWViewer/m'hul:hlrps%3A%2F%2F737ied>lee-Alabdn-dlmwlWSLseqnenmerbghlspmem. 2/2