U.S. Smartphone Users Smartphone users, as a percentage of...

U.S. Smartphone Users Smartphone users, as a percentage of the population, are projected to be $$f(t)=18.952+14.088 \ln (t+1) \quad(0 \leq t \leq 5)$$ percent in year $t,$ where $t$ is measured in years, with $t=0$ corresponding to $2010 .$ What is the projected average percentage of the population that will be smartphone users over the period from 2010 through 2015?

U.S. Smartphone Users Smartphone users, as a percentage of the population, are projected to be
$$f(t)=18.952+14.088 \ln (t+1) \quad(0 \leq t \leq 5)$$
percent in year $t,$ where $t$ is measured in years, with $t=0$ corresponding to $2010 .$ What is the projected average percentage of the population that will be smartphone users over the period from 2010 through 2015?

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Key Concepts

Average Value of a Function

The average value of a function over an interval is determined by integrating the function over that interval and then dividing by the length of the interval. This technique is fundamental in calculus and is widely used to obtain a single representative value from a continuously varying function.

Definite Integral

A definite integral calculates the accumulation of a quantity, or the area under a curve, over a specific interval. It is a central concept in calculus that is used to evaluate total quantities, such as average values and net changes, in various applications.

Integration of Logarithmic Functions

Integrating logarithmic functions typically requires the use of integration techniques such as integration by parts. Mastery of these techniques enables the analysis and solution of problems where logarithmic functions model growth or decay processes, making them crucial in applied calculus.

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