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?

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1. f(n) = 8(1.05)^n, sorry

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2. PART A:
f(n) = 8 × (1.05)^n
At n = 0 days, the plant was 8 cm high, according to this rule.
(Note: 1.05^0 = 1)
The difference in growth is:
11.26cm - 8cm = 3.26cm
The time taken for this extra growth is found from:
3.26 = 8×(1.05)^n
ln(3.26) = ln(8) + n ln(1.05)
1.18 = 2.08 + 0.05n
This gives a negative value of n. Please check the problem statement again and be certain that you have the correct equation!
PART B:
x represents time, y represents height of plant
PART C:
At n = 2, the height of the plant is 8×(1.05)^2 = 8.82 cm
At n = 6, the height of the plant is 10.72 cm
The average rate of growth is:
(10.72 - 8.82)/(6 - 2) = 1.9cm/4days
But again, I am using the equation you supplied. This equation needs to be checked very carefully!

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3. The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Emerson is studying the change in the amount of money in two accounts, A and B, over time.

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 1,264(1.09)x

Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.

r (number of years) 1 2 3 4
g(r) (amount in dollars) 1,375 1,512.50 1,663.75 1,830.13

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4. The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Emerson is studying the change in the amount of money in two accounts, A and B, over time.

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 1,264(1.09)x

Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.

r (number of years) 1 2 3 4
g(r) (amount in dollars) 1,375 1,512.50 1,663.75 1,830.13

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