Abiologist is studying the growth of a particular species of algae. she writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 7(1.06)d part a: when the biologist concluded her study, the radius of the algae was approximately 13.29 mm. what is a reasonable domain to plot the growth function? (4 points) part b: what does the y-intercept of the graph of the function f(d) represent? (2 points) part c: what is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)

Function: radius = f(d) = 9 * [1.04] ^ d a: domain it is the possible values of d, which are from 0 (just before the study starts) to the value d that makes f(d) = 12.81 => 12.81 = 9 * [1.04]^d => [1.04]^d = 12.81 / 9 = 1.4233 take ln to both sides to find d: d ln[1.04] = ln [1.4233] => d = ln [1.4233] / ln [1.04] = 9.00 so, the study lasts until the day 9, and the domain is the interval [0, 9] b) the y - intercept is the value of the function when d = 0, so it represents the radius of the algae at start. it is f(0) = 9 * [1.04]^0 = 9. which means that the initial radius of the algae is 9 mm. c) find the values of the function when d = 3 and when d = 9. d= 3 => f(3) = 9 *[1.04]^3 = 10.12 mm d = 9 => f(9) = 12.81 mm rate of change = [change in radius] / [number of days] = rate of change = [12.81mm - 10.12mm] / [9 days - 3 day] = 2.69 mm / 6 days rate of change = 0.448 mm/days. it represents the average change of radius per day.