Question

The number of visitors p to a website in a given week over 1-year period is given by p(t)=119+(t-83)e^0.02t , where t is the week and t is greater than or equal 1 and less then or equal 52.a)over what interval of time during the 1-year period is the number of visitors decreasing?b)over what interval of time during the 1-year period is the number of visitors increasing?c)find the critical point, and interpret its meaning.

Answer 1

The function p(t) for the number of visitors over 1-year is an exponential function

• The increasing interval is: [33,52]
• The decreasing interval is: [0, 33]
• There is no critical point

The increasing and the decreasing interval

The function is given as:

p(t) = 119 + (t-83)e^0.02t

Start by plotting the graph of the function p(t).

From the graph (see attachment), we have the parameters to be:

• Increasing: [33,52]
• Decreasing: [0, 33]
• Critical point = None

Hence, the function has no critical point

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