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)

Answer 1

someon please help

Answer 2

Do you know what the domain of a function is?

Answer 3

Part A:
To find a reasonable domain, set the y value to the maximum height of the plant.
11.26=8(1.05)n
n=11.26/(8(1.05))
n=1.34
Because the plant cannot be a negative height, our minimum for the domain must be 0.

The domain of the function should be [0,1.34]

Part B:
The Y intercept of the function represents the time, in days, when the plant had a height of 0.

Part C:
Average rate of change, A.K.A the slope of the function. is 8*1.05=8.4
This represents how much the plant grew each day. (8.4cm)

Answer 4

The function is written above as f(n) = 8(1.05)n.
That makes no sense. If the 8 and the 1.05 and the n are just factors in a multiplication, then it could easily be written as
f(n) = 8.4n

Is the function really

\(f(n) = 8(1.05)^n\) ?

If so, get used to writing exponents properly because O.S. helpers can't guess what you mean, and then just waste time trying to help you with an incorrect equation.