Math 115 Lab #9
M. Flashman Fall '07
I. Graphs of "Simple" Exponential Functions
II. What is e? What is exp(x)
- Tools for Winplot used in this lab:
- Equation menu
- Animation menu
- Families on Inventory.
I.Graphs of Exponential Functions
Record your answers for the next work and submit them on Moodle by Wednesday, November 14th.
- Set the parameters: A= 1 and B=2.
- Plot the point (h, B^h)
- Plot the point (h, A*B^h)
- Plot graphs with explicit for
- y = f(x) = B^x
- y = g(x) = A*B^x
- Use animator A; family A.
- Set A = 1, use animator for B; family B.
- The base of the function g is B.
- Since B^(r+s) = B^r * B^s, B^(x+s) = B^x * A where A = B^s.
- Since B^(k*r) = (B^k)^r, B^(kx) = B'^x where B' =B^k.
Find A and B where y=A*B^x with y(0)=7, y(1)=21.
Find A and B where y=A*B^x with y(1)=20, y(2)=100.
Find x where 5*3^x =45.
- Find an estimate for x where 3* 7^x = 210. [Use Winplot]
- Find an estimate for any and all x where 2^x + (1/2)^x = 10. [Use Winplot]
End of Lab 9
|II. Not covered in LAB!
What is e? What is exp(x)?
- Make a spead sheet showing the values for (1 +
1/n)^n where n = 1, n=10, n=100, n=1000, ... , n = 1000000.
Continue your spread sheet until n = 10^20.
- Record your result (approximately) for n= 1000000 and n = 10 ^20.
- Using winplot
- Plot ( 1, (1+1/n)^n
- Graph y = ((1+1/n)^n)^x.
- Graph y = exp(x).
- Compare the graphs.