1.
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) = 12(1.04)n

Part A: Is this a growth or decay exponential function? Justify your answer. (2 points)

Part B: What is the growth or decay percentage for this function? (2 points)

Part C: What does the y-intercept of the graph of the function f(n) represent? (2 points)

Part D: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

Question

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fichoh fichoh · Answer 1 · 2020-12-13T01:40:14+01:00

Answer:

Exponential growth

4%

12

Step-by-step explanation:

Given the function :

f(n) = 12(1.04)^n

Part A: Is this a growth or decay exponential function?

The equation above is usually generally represented as :

F(n) = A(1 ± r)^n

Where F(n) = final amount after n years ; r = rate ; n = number of years

The function Given above is thus :

F(n) = 12(1 +0.04)^n

This is an exponential growth function because of the negative rate (+ 0.04)

Part B: What is the growth or decay percentage for this function

From the equation :

F(n) = A(1 + r)^n ; r = rate

Comparing F(n) = 12(1 +0.04)^n ; r = 0.04 = 0.04*100% = 4%

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

The y intercept :

Value of F(n) when n = 0

F(n) = 12(1 +0.04)^n

F(n) = 12(1 +0.04)^0

Fn = 12(1)

Hence, intercept = 12