Question

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) = 3(1.09)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 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 = 2 to m = 8, and what does it represent?

Answer 1

f(m) = 3 * 1.09 * m = 3.27 * m

A:

solve f(m) = 5.98 to find how long it takes for fish to reach that length

5.98 = 3.27 * m

m = 5.98/3.27 = 1.83 months

A reasonable domain would technically depend on other factors like standard deviation, however, a domain of [0,3] could be reasonable without further information.

B:

The y intercept (0 because f(0)=0 ) represents the length of fish at the beginning of the marine biologists study, or when the number of months is zero

C:

Rate of change equals the change in y over the change in x.

`(f(8)-f(2))/(8-2)=(26.16-6.54)/(6)=(19.62)/(6)=3.27(cm)/(month)\\`

This represents the average number of cm the length of the fish change per month in the interval [2, 8]