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Log-Applications

# Log-Applications - Applications of Exponential and Log...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Applications of Exponential and Log Equations Exponential and Logarithmic functions have perhaps more real-world applications than any other class of functions at the pre-calculus level and beyond. These functions govern population increase as well as interest income in a bank. And since (it seems) virtually everything decays exponentially, we can apply exponential decay equations to many different applications (see http://www.mathmotivation.com/science/carvalue.html ) Exponential Growth and Decline: Exponential growth and decline is governed by the function: N(t) = N o e kt where N o = the original amount at time t=0. k = the (decimal) rate of growth per time period, be it years, days, etc. t = the units used in the time period. N(t) = the amount at time t NOTE: N(t) means “N as a function of t”, NOT “N times t”! Example: A population grows exponentially 3% per year. If the population is initially 1000, how many years will it take for the population to double to 2000? How many years will it take for the population to reach 4000? Since the original amount is 1000, N o =1000. Also, we know that N(t) = 2000 and also N(t) = 4000. In both cases, k = 0.03 . So we have to solve the equations: 2000 = 1000e 0.03t and 4000 = 1000e 0.03t .

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