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

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough