Topic 5 This table shows the number of coyotes in a park since 2000. Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 No. 71 124 168 208 249 280 312 337 362 381 405 (1) Estimate the instantaneous rate of change in the number of coyotes in 2005. (2) If a quadratic function for the number of coyotes in terms of time (f = 0 for 2000) is obtained as f(1) =-1.8/ + 50.5t + 74.1, find the instantaneous rate of change in 2005. [31.5 C/yr, 32.48 C/yr] 2 A penny is tossed upward from a cliff that is 80 m above the water. Its height above the water is modelled by h(1) = -5r + or + 80, where h(t) is the height in metres and ? is time in seconds. (a) Calculate the average rate of change in height during each of the following time intervals. OSIS1 1SIS2 25153 (b) Why is not the average rate of change constant as the time increases? (c) What does this average rate of change represent here? [1, -9, -19, -29 m/s; -10 m/s'; *], 5 Computers lose value rapidly over time. Sean buys a computer at $1920 and it is worth only $600 after 3 year. What is the average annual rate of change in the value of the computer for the 3 years? [-32.1%/yr]