Suppose that in a certain area the consumption of...

Suppose that in a certain area the consumption of electricity has increased at a continuous rate of $6 \%$ per year. If it continued to increase at this rate, find the number of years, to the nearest tenth, before twice as much electricity would be needed.

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Key Concepts

Exponential Growth

Exponential growth is a process in which a quantity increases by a consistent percentage over equal time intervals. This type of growth is characterized by the fact that the rate of increase is proportional to the current amount, resulting in rapid increases over time.

Continuous Compound Growth

Continuous compound growth is modeled by the formula A(t) = A?e^(rt), where A? is the initial amount, r is the continuous growth rate, and t is the time. This concept illustrates growth that occurs at every moment, rather than at discrete intervals.

Doubling Time

Doubling time is the period needed for a quantity undergoing continuous exponential growth to double in size. The double is found by setting A(t) equal to twice the initial amount and solving for t, typically involving the use of logarithms.

Natural Logarithm

The natural logarithm, which has the base e, is commonly used for solving equations involving exponential growth. It allows for isolating the variable in the exponent, making it essential for computing time periods like the doubling time.

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