Scenario 2:
You are looking to invest in Nike stock. The following equations represents what were the stock prices were last year. Put the following equations into desmos, analyze, and answer the following questions:
\[
\text { Nh } \begin{array}{l}
y=25 \cdot(2)^{x}+45\{0< x< 2\} \\
y=-\frac{1}{2} x+146(0< x< 10\} \\
y=-x+150(8< x< 20\} \\
y=-2(x-15)(x-40)\{17.9< x< 35\} \\
y=-\frac{1}{5}(x-50)^{2}+250\{34.2< x< 80\}
\end{array}
\]
* What is the highest price did Nike reach?
- What time frame did the stock increase at the fastest rate?
What time frame(s) did it decrease?
1. At the end of the graph, would it be a good idea to buy the stock? Why or why not?
Answer
1. \text{Not a good idea to buy at the end because the stock is decreasing when } 34.2 < x < 80.
Step 1 ：\(y_{max} = \max\{\max(25 \cdot 2^{x} + 45), \max(-\frac{1}{2} x + 146), \max(-x + 150), \max(-2(x-15)(x-40)), \max(-\frac{1}{5}(x-50)^{2}+250)\}\)
Step 2 ：\text{Fastest rate}: \(0 < x < 2\)
Step 3 ：\text{Decrease time frames}: \(0 < x < 10\), \(8 < x < 20\), \(17.9 < x < 35\), \(34.2 < x < 80\)
Step 4 ：1. \text{Not a good idea to buy at the end because the stock is decreasing when } 34.2 < x < 80.
