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?

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

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!