Exponential Equations and Applications
This final page covers solving exponential equations using logarithms and introduces applications to growth and decay models. It provides logaritmi esercizi svolti pdf (solved logarithm exercises in PDF format) style examples.
For exponential equations, the key technique is to apply logarithms to both sides:
Example: Solve 5^(x+1) = 3^(2x)
Solution: log(5^(x+1)) = log(3^(2x))
(x+1)log(5) = 2x·log(3)
Solve for x
The page then introduces exponential growth and decay models:
Definition: N(t) = N_0 · e^(kt), where N_0 is the initial quantity, k is the growth/decay rate, and t is time
Example: A bacteria population of 500 doubles every 20 minutes. How many bacteria will there be after 25 minutes?
The solution involves determining the growth rate k using the doubling time, then applying the model equation.
Highlight: Exponential models are widely used in biology, finance, and physics to describe phenomena that grow or decay at a rate proportional to the current amount.
The page concludes with exercises on determining the time required to reach a certain population or value, reinforcing the practical applications of logarithms and exponential functions.