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.

Question

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) = 13.86t^0.535

percent of the population.† (Round your answers to two decimal places.)

(a) What percentage of the U.K. population is expected to watch video content on mobile phones in 2016?

(b) How fast is the percentage of mobile phone video viewers in the United Kingdom in 2016 expected to change?

Answer 1

Hello Gabrielle,

PART A:

1. For the year 2016: t=5
2. Enter t=5 into the given equation: P(5) = 13.86*(5)^0.535 = 32.79%

PART B:

The question asks for the instantaneous rate of change for the year 2016 (t=5). We need the derivative of P(t) for this. This function requires only the power rule for the derivative. To get the derivative:

1. Multiply by the current power and subtract one from it: P'(t) = 13.86*0.535*t^0.535-1
2. Simplify: P'(t) = 7.4151*t^-0.4650
3. Rewrite the equation in step #2 to have the variable, and its power, in the denominator with a positive exponent. Positive exponents are considered "simplified." I will use the equation as it appears in step #2, though, to keep things clear while typing the solution.
4. Plug in t=5 into the derivative P'(t) => P'(5) = 7.4151*(5)^-0.4650 = 3.51 % per year

Let me know if I can help more :)