Question

Please help with these questions!

can someone walk this through with me?

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?

Part B: What does the y-intercept of the graph of the function f(n) represent?

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?

Answer 1

Explanation:

PART A:
A reasonable domain is 0
`\leq` x
`\leq` 7
The point 11.26 is at 7.006, or just 7 if rounded. Because of this, 7 is the highest number it can be.
PART B:

The y-intercept represents the original height of the plant.
The y-intercept is 0,8 or 8 inches at the very beginning, therefore it is the height of the plant.
PART C:
The average rate of change is .475.
8(1.05)^2 = 8.82
8(1.05)^6 = 10.720765125 or approximately 10.72.

`(f(b) - f(a))/(b - a)` is the formula for calculating rate of change, so you would take the number of days and plug them into b and a, and the answers would plug into f(b) and f(a).

Therefore, you would have
`(10.72 - 8.82)/(6-2)` which would get you to
`(1.9)/(4)`, or approximately .475.