7. Your neighbor joins the contest and posts a video of his puffer fish that has 100 views the first day, 200 views the second day, and 400 views the third day. Modeling this growth as before, you get the following equation: If that growth rate continues for the next 14 days, will the puffer fish video have more or fewer views than the total number of views for your friend's video? Will you create a table of values or use the Sum of a Geometric Series Tool to find your answer? Explain which method you will choose, and find out who will win the contest. (3 points: 1 point for the explanation, 1 point for the sum after 14 days, 1 point for the comparison) The equation was a n = 100(2)^n-1

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?