Do 5 & 6, a & b

Days 4 9 10 14 16 20 30 Number of Views 2 100 127 177 200 210 240 253 273 309 (in thousands) 5. A student uploads a short video to TikTok. The number of views (in thousands) t days after the upload can be modeled by the logarithmic function V(t). The table above shows the total number of views at selected values of t. a) Use the regression capabilities on your graphing calculator to find the logarithmic model V(t) = a + b Int, where V represents the total number of views, in thousands, t days after the student uploaded the video. b) Using the model found in part a, how many days will it take for the student's video to reach 500,000 total views? 6. The most common method to measure the magnitude is the Richter scale, developed by Charles Richter in 1935. The Richter scale gives output values (magnitude of the earthquake) based on the maximum ground displacement measured by a seismograph that is a given distance away from the epicenter of the earthquake. However, the Richter scale modeled based on data specific to Southern California and is not always a reliable way to measure earthquakes. Several improved models have been introduced since 1935, including the Lillie Empirical Formula. If a seismograph is positioned 200 km away from the epicenter of an earthquake, the Lillie Empirical Formula can be modeled by M, = a+ blogx, where x represents the maximum ground displacement measured by the seismograph measured in microns (um). For a seismograph positioned 200 km away from the epicenter, an earthquake of magnitude M, =5.2 will create a maximum ground displacement of 21 um, and an earthquake of magnitude M, =6.1 will create a maximum displacement of 180 um. a) Write two equations that can be used to find the values for constants a and b in the expression for M, . Find the values of a and b. b) The largest recorded earthquake in history was the Great Chilean Earthquake on May 22, 1960. This earthquake had a magnitude of M, =9.5! Using the model found in part b, what was the maximum ground displacement , in microns, measured by a seismograph positioned 200 km from the epicenter