An example of an exponential function is the voltage as a function of time Vf(t) as the capacitor C1 discharges from an initial voltage Vi to a resistive load R1. The circuit of this is shown below
Figure 1. Discharge of Capacitor
Where
Vf is the final voltage
Vi is the initial voltage across the C1
Table 1. Calculated and Oscilloscope Voltages
Figure 2. Calculated Voltages
Figure 3. Oscilloscope Voltages
Logarithmic Function
An example of an logarithmic function is the Sound Pressure Level which is expressed in decibels.
SPL = 20 log(P/P0) (dangerousdecibels. org, 2005)
Where:
SPL is the sound pressure level in decibels
P0 is the reference threshold of hearing, 2 x 10 -5 N/m 2
P is the measured pressure amplitude in N/m 2
Table 2. Calculated and Measured Sound Pressure Levels
Figure 5. Calculated Sound Pressure Levels
Figure 6. Measured Sound Pressure Levels
Appendix
Spreadsheet for Exponential Function
Spreadsheet for Logarithmic Function
References
” Sound Measures”. DangerousDecibels. org website: http:// www. dangerousdecibels. org/teachers_guide/DDB_TRG_Activities_10. pdf on May 1, 2007