Assignment 11
1. Show how the rules for log(a*b) and log(an) come from rules for exponents.
2. Write (1/2)t/350 in terms of the exponential function.
3. Assuming monthly compounding, how long does it take money invested at 5% to double? Repeat for continuous compounding.
4. We wish to fit the data below to a curve of the form N = A (1/s)d. Take the log to get a linear equation for log(N) to fit, and then fit the data to this problem. Plot the original data, and the fitted curve.
N |
s |
28 |
¼ |
83 |
1/8 |
246 |
1/16 |
746 |
1/32 |
5. Solve the following for x.
a. ln(x2)=3
b. 2x = 104-x
c. logx(2)=1.5
6. pH is defined as –log10(concentration of H+ ions in moles per liter). If a liquid has pH = 5.3, what is the H+ concentration?
7. If f(x) = 3x, what is f-1? Graph both on the same axes.