- The function \(f( t) = 1900( 1.075) ^ { t/60} \) is in the form \(f( t) = A \cdot B^ { t/C} \), where \(B = 1.075\) and \(C = 60\).
- The base \(1.075\) indicates the factor by which the quantity increases for every \(C\) seconds.
- Since \(B = 1.075\), this means the quantity increases by 7.5% every 60 seconds.
Therefore, the function is increasing exponentially at a rate of 7.5% every 60 seconds.
Supplemental Knowledge
Exponential functions are used to model situations where a quantity grows or decays at a rate proportional to its current value. The general form of an exponential function is \(f( t) = A \cdot ( 1 + r) ^ t\), where \(A\) is the initial amount, \(r\) is the growth (or decay) rate, and \(t\) is time.
Everyday Examples
Exponential functions play an integral part in everyday situations like population growth, radioactive decay and interest calculations. Understanding investments that grow over time with compound interest entails using exponential functions as part of understanding their growth trajectory.
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