Ascientist is studying the growth of a particular species of plant. he writes the following equation to show the height of the plant f(n), in cm, after n days: f(n) = 8(1.05)n part a: when the scientist concluded his study, the height of the plant was approximately 11.26 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(n) represent? part c: what is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent?

A. alright, domain is the nymbers you can use for the variable
in this case, the domain is n which represents the number of days
you don't say "it's been 3.45 days" or "it's been -2.3 days" so we use only whole numbers

the domain is all whole numbers



b. that is where the graph crosses the y axis or where n=0
that is the height of the plant after 0 days, so that is the initial height of the plant



c.
just find the slope from (2,f(2)) and (6,f(6))

that is (f(6)-f(2))/(6-2)=
(f(6)-f(2))/4=
(8(1.05)^6-8(1.05)^2)/4=
(8((1.05)^6-(1.05)^2))/4=
2((1.05)^6-(1.05)^2)
use your calclator
0.475192

it represents the average rate of grouth per day of the plant from day 2 to 6