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) = 11(1.01)d
part a: when the biologist concluded her study, the radius of the algae was approximately 11.79 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 = 2 to d = 7, and what does it represent? (4 points)

we are given the function of growth:

f (d) = 11 (1.01)^d

or

r = 11 (1.01)^d

where r is the radius of the algae and d is the number of days

part a. find the domain to plot the function:

we can set-up to restrictions in the function, these are:

d = 0                                        (at time zero before the growth occurs, let us call this d1)

r = 11.79                            (the radius of algae at the end of the study, let us call this r2)

so we have the initial domains:

(r1, 0) and (11.79, d2)

let us find for r1 when d = 0:

r1 = 11 (1.01)^0

r1 = 11

find for d2 when r = 11.79

11.79 = 11 (1.01)^d2

d2 log  1.01 = log (11.79 / 11)

d2 = 6.97

hence the domains are:

(11, 0) and (11.79, 6.97)

part b. the y-intercept is the value of r when d = 0, this is r1 = 11. this is the radius of the algae before the study started (initial radius).

part c.

f(2) = 11 (1.01)^2 = 11.2211

f(7) = 11 (1.01)^7 = 11.7935

average rate of change = [f(7) – f(2)] / (7 – 2)

average rate of change = 0.1145 mm / day

this represent the slope of the graph from d = 2 to d = 7.

answer: a and b

step-by-step explanation: