It is observed that a certain bacteria culture has a relative growth rate of 14% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 25. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.) (a) No antibiotic is present, so the relative growth rate is 14%.

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?