1) The spread of a virus in an isolated community is modeled by N(t)=1100/1+49e^-0.3t, where N(t) is the number of people infected after t days.
a) Approximately how many people will be infected in 16 days?
b) How long until 900 people have been infected? Round to the nearest day.
2) Solve for x: 2^5x-4=3^7x+4
Round to the nearest 0.001.
3) The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of organic matter can be used to determine the age of the organic matter. Archaeologists discovered a linen wrapping from an ancient scroll had lost 24.2% of its carbon-14.
a) If the model A=Ce^kt is used to model the amount of carbon-14 present at time t, determine the value of k. Round to five decimal places.
b) Use the model to estimate how old the linen wrapping was when it was found. Round to the nearest year.
The solution contains the solution to the given problems.