Part One:
Dear Marty the Mart Mart,
This mysterious variable ‘e’ that your teacher speaks of is equal to 2.171828 and it continues on forever. Credit for discovery of this variable goes to Jacob Bernoulli. Your brother was correct in saying that ‘e’ is used in calculus; ‘e’ is used with exponential functions, logarithms, and the graphing of them. Your teacher was right, it is also used in banking. The formula (A=Pert) to calculate how much money your bank account makes from interest over time uses ‘e’.
Real life examples of Exponential Growth
- Internet traffic
- Viruses or diseases spreading
- Investing money
Real life examples of Exponential Decay
- Atmospheric pressure (with increasing height above sea level)
- Electric charge stored on a capacitor
- In pharmacology and toxicology
I hope this helps you along your journey through the wonderful world of calculus, Marty.
Sincerely,
One who is not exponentially confused
Part Two:
1. 
If you look at this wave sideways, it is exponentially growing until the tip of the wave.
2. To solve this problem, you will use the compound continuous formula, A=Pert.
A= Final Amount, P= Principal amount, r= interest rate as a decimal, t= number of years (time)
-Plug the values that you know into the formula.
A= 500e(.035 x 10)
(.035 x 10)= .35
(500e)(.35)= $709.53
A= $709.53
3. To solve this problem, you will use the formula A=P(1+ r/n)nt
A= Final amount, P=Principal amount, r= interest rate as a decimal, n= number of times compounded in a year, t= number of years (time)
-Plug known values into the formula.
A=500(1+.035/4)(4 x 10)
(.035/4)= .00875
(1 + .00875)=1.00875
(1.00875)40= 1.4169
(1.4169) x (500)= $708.45
A= $708.45
Part Three:
Black: 3sin(x)
red: 1.5cos(x)2sin(x)
blue: tan(x)cos(x)
green: -csc(x)
orange: tan(x)
Part Four:
You might be in Honors Algebra II if you think that Jumbo Ozaki is perhaps the coolest name on the face of the Earth, you insult someone by calling them an “angle-side-side,” you enjoy bitterly sarcastic conversations, you know what the “Trucker Wagon” is, and you also feel the need for all markers to be well saturated or else they get thrown into the trash can.
