Just with part c
a scientist 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) = 12(1.03)n
part a: when the scientist concluded his study, the height of the plant was approximately 16.13 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 = 3 to n = 10, and what does it represent? (4 points

I will assume you meant f(n)=12(1.03^n) for exponential growth

a)

If the study concluded when the plant was 16.13cm we need to find when the study ended...

16.13=12(1.03^n)

16.13/12=1.03^n  take the natural log of both sides

ln(16.13/12)=n*ln(1.03)

n=ln(16.13/12)/ln(1.03)

n≈10 

So the study lasted for 10 days, so the domain should be n=[0,10]

b)

The y-intercept, when n=0 is 12 cm, which is the initial height of the plant.

c)

The average rate of change is just the change in height divided by the change in days...

a=(f(10)-f(3))/(10-3)

a=(12(1.03^10-1.03^3))/7

a≈0.431cm/day

This is the linear approximation of the growth rate per day.