A house is purchased for $140,000 in January 2004. A year later, the house next door is sold for $149,800. The two houses are of the same style and size and are in similar condition, so they should have equal value. Use the model v = 140e^0.0676586485t, where t is the number of years after January 2004 and v is the value in thousands of dollars, to predict when the house would be worth $270,000.
a) The house will be worth $270,000 in (what month and year?)
2. A biologist is conducting an experiment that involves a colony of fruit flies. (Biologists frequently study fruit flies because their short lifespan allows the experimenters to easily study several generations.) One day, there were 2,730 flies in the colony. Three days later, there were 5,880.
(a) Develop the mathematical model that represents the population p of flies. (Write your model in terms of t, where t is measured in days. Round the coefficient of t to seven decimal places.)
p(t) =
(b) Use the model to predict the population after one week. (Round your answer up to the next whole number.) Flies:
(c) Use the model to predict when the population will be double its initial size. (Round your answer to one decimal place.) Days: