Question

date ____ period __
is it a good investment?

	whats happening?	buy, sell or hold?
large positive slope (m > 2)	price rising fast and breaking the limit
small positive slope (0< m <2)	slowly approaching highest limit and soon the price will go down
large negative slope (m < -2)	quickly approaching lowest limit and big sign it will pop back up
small negative slope (-2 < m < 0)	approaching the lowest limit of stock price

example 2
this table shows a stocks price over time.
what is the slope? will this be a good investment?
slope = \\(\frac{change\\,of\\,price}{change\\,of\\,time}\\) = \\(\frac{\delta p}{\delta t}\\)

day	stock price ($)
1	50
2	55
3	60
4	70
5	85

Explanation:

Step1: Calculate the slope

We use the formula for slope \( m=\frac{\Delta P}{\Delta t} \), where \( \Delta P \) is the change in price and \( \Delta t \) is the change in time. Let's take two points, say \( (t_1, P_1)=(1, 50) \) and \( (t_2, P_2)=(5, 85) \). Then \( \Delta P = 85 - 50=35 \) and \( \Delta t = 5 - 1 = 4 \). So \( m=\frac{35}{4}=8.75 \).

Step2: Determine the investment decision

Since \( m = 8.75>2 \), it has a large positive slope. From the table, when there is a large positive slope (price rising fast and breaking the limit), the decision is to buy.

Answer:

The slope is \( 8.75 \), and it is a good investment (decision: Buy).