The consumption of electricity has increased historically at...

Name: Problem 75, Chapter 5: Finite Mathematics and Calculus with Applications
Uploaded: 2020-09-28T07:57:35-08:00
Duration: 43 s
Channel: Lourence Gonhovi
Description: The consumption of electricity has increased historically at 6% per year. If it continues to increase at this rate indefinitely, find the number of years before the electric utilities will need to double their generating capacity.

The consumption of electricity has increased historically at 6% per year. If it continues to increase at this rate indefinitely, find the number of years before the electric utilities will need to double their generating capacity.

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Key Concepts

Doubling Time

Doubling time is the period required for a quantity undergoing exponential growth to double in its size. It is calculated using logarithmic relationships and provides a practical way to understand the speed of growth. This measure is widely used in contexts like finance and natural phenomena to estimate when an amount will become twice its initial value.

Natural Logarithms

Natural logarithms, which use the mathematical constant e as their base, are essential tools for solving equations involving exponential growth. By applying natural logarithms, one can isolate and solve for time or rate variables in growth scenarios, making them indispensable in determining periods such as the doubling time in exponential processes.

Exponential Growth

Exponential growth refers to an increase in a quantity where the rate of change is proportional to the current amount, leading to growth by a constant percentage over equal time intervals. This concept is fundamental in various fields such as population dynamics, finance, and natural processes, where understanding how something increases rapidly over time is crucial.

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