As mobile phones continue to proliferate, more and more...

As mobile phones continue to proliferate, more and more people will watch video content on them through a mobile browser, subscription, download, or application at least once a month. In a study released in 2013 , eMarketer estimated that the number of mobile phone video viewers in the United Kingdom in year $t$ from $2011(t=0)$ through $2017(t=6)$ will be $$P(t)=13.86 t^{0.535}$$ percent of the population. a. What percentage of the U.K. population is expected to watch video content on mobile phones in $2015 ?$ b. How fast is the percentage of mobile phone video viewers in the United Kingdom in 2015 expected to change?

As mobile phones continue to proliferate, more and more people will watch video content on them through a mobile browser, subscription, download, or application at least once a month. In a study released in 2013 , eMarketer estimated that the number of mobile phone video viewers in the United Kingdom in year $t$ from $2011(t=0)$ through $2017(t=6)$ will be
$$P(t)=13.86 t^{0.535}$$
percent of the population.
a. What percentage of the U.K. population is expected to watch video content on mobile phones
in $2015 ?$
b. How fast is the percentage of mobile phone video viewers in the United Kingdom in 2015 expected to change?

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Key Concepts

Mathematical Modeling

This concept involves representing a real-world phenomenon using mathematical functions. In contexts such as predicting mobile phone usage, a function maps time to a specific percentage of the population exhibiting a behavior, allowing for quantitative analysis and forecasts.

Function Evaluation

This technique is the process of substituting a specific value into a function to compute its output. It is used to determine the expected outcome, such as the percentage of mobile video viewers at a particular time, by simply plugging the time variable into the model.

Differentiation

Differentiation is a core concept in calculus used to determine the rate at which a quantity changes with respect to another variable. In applied settings, this helps analyze how quickly a percentage of a population is increasing or decreasing over time.

Power Rule in Differentiation

The power rule is a fundamental method for differentiating functions of the form t^n, stating that the derivative is n*t^(n-1). This rule simplifies the process of finding the rate of change for functions that model phenomena with exponents, such as time-based predictions in population studies.

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