1.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) = 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?

PART A: 
f(n) = 8 × (1.05)^n 
At n = 0 days, the plant was 8 cm high, according to this rule. 
(Note: 1.05^0 = 1) 
The difference in growth is: 
11.26cm - 8cm = 3.26cm 
The time taken for this extra growth is found from: 
3.26 = 8×(1.05)^n 
ln(3.26) = ln(8) + n ln(1.05) 
1.18 = 2.08 + 0.05n 
This gives a negative value of n. Please check the problem statement again and be certain that you have the correct equation! 
PART B: 
x represents time, y represents height of plant 
PART C: 
At n = 2, the height of the plant is 8×(1.05)^2 = 8.82 cm 
At n = 6, the height of the plant is 10.72 cm 
The average rate of growth is: 
(10.72 - 8.82)/(6 - 2) = 1.9cm/4days