Comment on Activity 4
A good guess based just on the graph is `b=2.7`. Any guess in the range `2.6` to `2.8` is adequate. From Activity 3, you should have the approximate values `L(2)=0.693` and `L(3)=1.099`, so you could calculate `b` by linear interpolation:
| `(1.099-0.693)/(3-2)` | `=(1-0.693)/(b-2)` |
| `0.406(b-2)` | =`0.307` |
| `b` | `=2+(0.307)/(0.406)` |
| `=2.76` |
Keep in mind that this is a very crude approximation. First we approximated the curve with a line segment; second, our values of `L` are only approximate; and third (but less obvious), the subtractions in our difference quotients can cause loss of significant digits. (See Section 1.6.) Thus, the calculation really only suggests that the value of `b` we seek is likely to be in the range from `2.7` to `2.8`.