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) = 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?

Answer 1

Answer:

It will be helpful to you

Answer 2

Given:

f(d) = 11(1.01)d

To Find:

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?

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 = 2 to d = 7, and what does it represent?

Solution:

Part A:

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 x 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

Hence, reasonable domain to plot the growth function is 6.97, the y-intercept of the graph of the function f(d) represents f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114.