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) = 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?

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

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?

Answer 1

Hello and welcome.

Asked and Answered here: https://questioncove.com/updates/5db1ab9d323a68b899c3f600

Answer 2

The question is different

Answer 3

This one has 1.08

Answer 4

The one you showed me has 1.09

Answer 5

in the question

Answer 6

Okay then just follow the steps but do it with 1.08 instead.

Answer 7

-_-
I've tried and I've been stuck for at least 37 mins

Answer 8

Hello Welcome
Do you still need help? If not please close

Answer 9

\[6.86=4(1.08)^m,\]\[(1.08)^m=\frac{ 6.86 }{ 4}=1.715\]
\[m \ln (.08)=\ln(1.715)\]
\[m=\frac{ \ln 1.715 }{ \ln 1.08 }\approx7.0089\]
so domain is 0<m<7.1

Answer 10

b. when m=0
\[f(m)=4(1.08)^0=4\times1=4\]
so y intercept is 4
average rate of change for m=3 to m=7 is
\[=\frac{ f(7)-f(3) }{ 7-3 }\]
\[=\frac{ 4(1.08)^7-4(1.08)^3 }{ 7-3 }\]
\[=\frac{ 4(1.08)^3[(1.08)^4-1] }{ 4 }\]
\[=(1.08)^3[1.08^4-1]\approx 0.454 cm\]