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) = 5(1.07)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 9.19 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 = 1 to m = 9, and what does it represent? (4 points)

The original function is f(m) = 5(1.07)^m, with the m as an exponent  

part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m  plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9  

part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent  part C) average rate of change from m = 1 to m = 9

part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent  part C) average rate of change from m = 1 to m = 9

Part A: The reasonable domain is [0,8]

f(m) = 3(1.09)^m

at 0 months f(0) = 3(1.09)^0

f(0) = 3

The fish was approximately 5.98cm  

5.98 = 3(1.09)^m

5.98/3 = 1.09^m

1.993 = 1.09^m

1.993 = 1.09^8

1.993 = 1.993

m = 8

Part B: The y-intercept is the initial length of the fish, which is 3cm.

f(0) = 3(1.09)^0

f(0) = 3

Part C: The average rate of change from 2 to 8 months is approximately 0.40

m = 2

f(2) = 3(1.09)^2

f(2) = 3*1.1881

f(2) = 3.5643

f(8) = 3(1.09)^8

f(8) = 3(1.9926)

f(8) = 5.9778

(5.9778-3.5643)/(8-2)

2.4135/6

0.4023

the first option i believe

step-by-step explanation: