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Question

Griffin Logan

11/11/2023 · Middle School

The function f(t)=1900(1.075)^ t/60 represents the change in a quantity over t seconds. What does the constant 1.075 reveal about the rate of change of the quantity?

The function is ___exponentially at a rate of___% every ___.

Answer
expertExpert-Verified Answer

Mccoy Ortiz
Specialized Tutor
5.0 (47votes)

The function is increasing exponentially at a rate of 7.5% every 60 seconds.

Solution

  1. 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 \(C = 60\).
  2. The base \(1.075\) indicates the factor by which the quantity increases for every \(C\) seconds.
  3. 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.

 

To master concepts like exponential growth and decay and other mathematical skills, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services. Our resources provide detailed explanations and interactive learning experiences tailored to your needs.
For those looking to enhance their mathematical skills further, UpStudy offers comprehensive guides that make learning both engaging and effective!

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