Question

A biologist 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?

Part B: What does the y-intercept of the graph of the function f(d) represent?

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?

Answer 1

Answer:

d = 6.97

d = 6.97f(d) = 11

d = 6.97f(d) = 110.114

Step-by-step explanation:

f(d) = 11(1.01)^d

Part A:

f(d) = 11.79

11.79=11(1.01)^d

(1.01)^d = 11.79/11

(1.01)^d = 1.071818

d = log 1.071818 /log 1.01

d = 6.97

Part B:

y- intercept is obtained when domain = 0

d = 0 ⇒ f(0) = 11(1.01)^0 = 11*1 = 11

f(d) = 11

Part C:

Average rate of change

Δf/Δd=

(f(7) - f(2)) / (7 - 2) =

(11(1.01)^7 - 11(1.01)^2) / 5 =

0.57 / 5 =

0.114