The video of the award incident was posted on social media. Once it reached a certain number of views it went viral! A video gets listed as on the site as "trending" when it has been viewed 100,000 times. The number of views V , in thousands, as a function of time t hours after the video started trending can be modeled by a piecewise function, which we will investigate below. A table of some values is given.

t (hours). V (1,000s of views)

0 100

10 120

20 144

a) Write a formula for an exponential function f(t) that could reasonably used to model V as a function of t for 0 t 24. Make sure to show that the model matches all of the data you are given.

b) What is the percent growth rate per hour? Give your answer both in exact form and as a decimal rounded to the nearest hundredth.

c) You may use a calculator (such as Desmos.com) to answer the following question: if the number of views continues to be an exponential function of t, about how long will it take to reach 200,000 views?

d) After trending for 24 hours, with views continuing to be modeled by f(t), the video stops trending. How many views has it received at this time?

e) After the video stops trending, V is best modeled by a linear function. Furthermore, when t = 30, V = 160. Using this information, write a formula for a linear function g(t) that can reasonably model V for t > 24.

f) With this new information, about how long would it take for the video to reach 200,000 views?

g) 40 hours after the video started trending, it is removed from the web and therefore receives no more views. Write a piecewise-defined formula for V that is valid for all positive values of t.