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? (4 points)
part b: what does the y-intercept of the graph of the function f(n) represent? (2 points)
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? (4 points)

part a.   n ∈ [0,7]

part b.   8 cm is the initial height of the plant.

part c.   avg of 0.475 cm/day

step-by-step explanation:

we can easily plot the equation and look at the graph. , see attached picture

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?

we can look in the graph the point where we can find a value for f of 11.26 cm

f(7) = 8*(1.05)^(7) = 11.26 cm

n = 7 days

a reasonable domain would be

n ∈ [0,7]

part b: what does the y-intercept of the graph of the function f(n) represent? (2 points)

the y-intercept represents the point where the number of days that the plant has grown is equal to zero.

in this case, n = 0

f(0) = 8*(1.05)^(0) = 8 cm

this is the initial height of the plant.

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? (4 points)

the average rate of change represents the average value of growth of the plant.

f(2) = 8*(1.05)^(2) = 8.82 cm

f(6) = 8*(1.05)^(6) = 10.72 cm

10.72 cm - 8.82 cm = 1.9 cm

the plant grew 1.9 cm over 4 days.

(10.72 cm - 8.82 cm) / (6 - 2) day

(1.9 cm) / (4) day   = 0.475 cm/day

c

step-by-step explanation: