A lot of points... A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 4(1.08)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. 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(m) represent? (2 points)

Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)

A marine biologist is studying the growth of a particular species of fish

: When the marine biologist concluded her study,  the length of the fish was approximately 9.19 cm

Step-by-step explanation:

easonable domain to plot the growth function

What does the y-intercept of the graph of the function f(m) represent?

average rate of change of the function f(m) from m = 1 to m = 9,

Step-by-step explanation:

PART A: 

f(m) = 3(1.09)^m

5.98 = 3(1.09)^m

(1.09)^m = 5.98 / 3

(1.09)^m = 1.9933

log (1.09)^m = log 1.9933

m log 1.09 = 1.9933

m log 1/9933 / log 1.09

m = 8 

So clearly the reasonable domain to plot is m = 8.

PART B:

m = 0   f(0) = 3(1.09)^0 = 3 x 1 = 3

f(0) = 3

Thats the starting point when the fish is 3 cm long.

PART C:

delta f / delta m

(f(8) - f(2)) / (8 - 2) = 

(3(1.09)^8 - 3(1.09)^2) / 6 = 

2.4133 / 6 =

The answer should be 0.40 (I rounded it, it would be 0.402216667)