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?

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

Answer 1

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Answer:

  A. 0 ≤ n ≤ 7

  B. the height after 0 days (the initial height in cm)

Step-by-step explanation:

A.

The plant cannot be expected to continue its exponential growth curve, so a reasonable domain is the domain of the observations already made. The plant reached its height of about 11.26 cm after about 7 days. The reasonable domain for the growth function is ...

  0 ≤ n ≤ 7

__

B.

The y-intercept corresponds to the n=0 value, the height of the plant at the start of the study.

_____

Additional comment

The value of n that gives f(n) = 11.26 can be found using logarithms.

  11.26 = 8(1.05^n)

  log(11.26/8) = n·log(1.05) . . . . . . divide by 8, take logs

  n = log(11.26/8)/log(1.05) ≈ 7.00582