HELP ME PL 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)

see below

Step-by-step explanation:

f(m) = 5(1.07)^m

A

9.19 =  5(1.07)^m

Divide each side by 5

9.19/5 =  5/5(1.07)^m

9.19/5 = 1.07 ^m

Take the log of each side

log(9.19/5)  = log 1.07 ^m

log(9.19/5)  = m log 1.07

Divide each side by log (1.07)

log(9.19/5) / log(1.07)  = m

8.99631 = m

Domain  runs from 0 to 9

b

The y intercept is when m=0

y =  5(1.07)^0

y = 5(1)

y = 5

The y intercept is 5 and is the starting height of the fish ( birth size)

c

f(1) = y =  5(1.07)^1 =5.35

f(9) = 5(1.07)^9 =9.19

average rate of change is

f(9) - f(1)

9-1

9.19 - 5.35

8

.48

This is the average growth rate  between 1 and 9 months

they are simplified

step-by-step explanation: