A news article states that the number of people infected with a particular virus has grown by 20% in one week which means 56 people became infected that week. 1. If the growth is linear, how many more people will be infected in one more week?       If the growth is exponential, how many more people will be infected in one more week?

If the national economy shrank at an annual rate of 12% per year for three consecutive years, then the economy shrank by 36% over the three-year period.What percentage did the economy shrink by?

9. The number of bacteria in a Petri dish grows exponentially, starting with just 1 bacterium, but reaching 500 after 72 hours. How many bacteria were there after the first 24 hours? At what rate was the number of bacteria growing after the first 24 hours?

Each machine on Widgetco’s assembly line gets out ofwhack an average of once a minute. Laborers are assignedto reset a machine that gets out of whack. The companypays each laborer cs dollars per hour and estimates that eachhour of idle machine time costs the company cm dollars inlost production. Data indicate that the time betweensuccessive breakdowns of a machine and the time to reset amachine are exponential. Widgetco plans to assign eachworker a certain number of machines to watch over andrepair. Let M total number of Widgetco machines, w number of laborers hired by Widgetco, and R Mw machines assigned to each laborer.a Express Widgetco’s hourly cost in terms of R and M.b Show that the optimal value of R does not dependon the value of M.c Use calculus to show that costs are minimized bychoosingR d Suppose cm 78¢ and cs $2.75. Widgetco has 200 machines, and a laborer can reset a machine in an aver-age of 7.8 seconds. How can Widgetco minimize costs? e In parts (a)–(d), we have…

In the year 1980, the city of Gumbolantenden had a population of 20,000. The population of Gumbolantenden grows at the rate of 1.07% each year. The population of the city of Attaliolo is growing exponentially. In the year 2000, the population was 40,000. In the year 2005, the population was 62,000. When will the populations of the two cities be equal?

A rabbit breeder starts with 16 rabbits. if the population grows exponentially at a rate of 23% per year how many years will it take for the breeder to have 58 rabbits?

Over the last year, a town's population increased from 190,000 to 249,000. If the population is growing exponentially at a steady rate, what will the population be one year from now

Personal care aide is an occupation that is growing quickly. Assume​ that, in a certain​ region, there will be a need for 195,686 personal care aides in​ 2024, a growth of about 29​% over 2014 levels. How many personal care aides were there in this region in​ 2014?

How could I find the number of years?

Personal care aide is an occupation that is growing quickly. Assume​ that, in a certain​ region, there will be a need for 150,146 personal care aides in​ 2024, a growth of about 25​% over 2014 levels. How many personal care aides were there in this region in​ 2014?