1.A fruit fly population of 182 flies is in a closed container. The number of flies grows exponentially, reaching 340 in 18 days. Find the doubling time (time for the population to double) to the nearest tenth of a day.
2.One thousand dollars is invested at 5% continuous annual interest. This means the value of the investment will grow exponentially, with k equaling the decimal rate of interest. What will the value of the investment be after 7 1/2 years?
3.A population grows exponentially, doubling in 4 hours. How long, to the nearest tenth of an hour, will it take the population to triple?
4.The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams?
Find the particular solution to y dx = x dy given that y(8) = 2.
x = 4y
y = 4y
6.Which of the following is a first-order homogeneous differential equation?
dy/dx = (3x^3-2x^2y)/xy^2
dy/dx=(x^2y^3 - y^5)/(2xy^5)