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? (4 points)

Question

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? (4 points)

ramirocruzo · Answer

Hi there....I'm not sure about Part I, but for part II,
On comparing with standard equation, y=mx + c,
Which in your case is, h=8.4n + 0
So, The y-intercept is 0.....

As the line plotted is linear, m is always constant... i.e. rate of change of h is constant &,
Rate of change of h=8.4

celinegirl · Answer

@RamiroCruzo ahh okay thank you!

celinegirl · Answer

Does this sound good for part A, my friend helped me so im not 100% sure if it is correct. 

(Domain ≥ n > because it means time.) Domain value of n, solve for g(n) = 11.26 we get 7.005 reasonable range to plot the graph would be from n = 0 to 8.