Given : 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
To Find : reasonable 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,
Solution:
m = 0
=> f(0) = 5(1.07)⁰ = 5 cm
the length of the fish was approximately 9.19 cm.
=>
=>
=> m = 9
Domain = [0 , 9 ]
reasonable domain to plot the growth function = [0 , 9 ]
y-intercept of the graph of the function f(m) represent represent initial length of fish = 5 cm
average rate of change of the function f(m) from m = 1 to m = 9
m = 1 => f(1) = 5(1.07) = 5.35 cm
m = 9 => f(9) = 5(1.07)⁹ = 9.19 cm
Change in 9 - 1 = 8 months = 9.19 - 5.35 = 3.84 cm
average rate of change of the function f(m) from m = 1 to m = 9,
= (3.84/8)
= 0.48 cm per month
Step-by-step explanation:
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
f(9)−f(1)9−1
evaluate, and think about what that represents in terms of height and number of months
