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Algebra Questions

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.
_________days

2) Solve for x: 2^5x-4=3^7x+4
Round to the nearest 0.001.
x=________

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.
k=_________

b) Use the model to estimate how old the linen wrapping was when it was found. Round to the nearest year.
__________years.

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