Question

WILL MEDAL AND FAN NEED HELP DESPERATELY
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) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 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 = 1 to n = 5, and what does it represent?

Answer 1

PART A)
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5

PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.

PART C)
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)

f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
(5, 11.040808)

Find the slope between those two points.

Answer 2

The slope represents how much the plant is growing every day.

Answer 3

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