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) = 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)

Answer 1

Is the equation supposed to be f(n) = 12(1.03)^n ?

Part A: f(p) = 12(1.03)^p = 16.13cm, solve for p by dividing both sides by 12 and the taking the log.

Part B: What x value does any y-intercept always have? Imagine a coordinate grid, if it helps. Imagine plugging that x-value into the equation - that x-value would be used for the n in the equation, where n is the number of days that have passed.

Part C: The average rate of change of M over time would be (M2 - M1)/(t2-t1), so find f(n) at n = 3 and n=10, and find the slope of the line between those points. By "what does it represent? ", I think they want you to explain about rate of change being between those two periods of time, 3 and 10 days past the start.

Does this make sense?

Answer 2

yes omg thank you