Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $50000 in the account. Each year the account earns 4% interest, and you deposit $5000 into the account. This can be modeled with the differential equation: dy dt y(0) Solve this differential equation for y(t) = y(t) = = 0.04y + 5000 50000

Suppose that P, is invested in a savings account in which interest is compounded continuously at 5.7% per year. That is, the balance dp P grows at the rate given by P = .057P(t) dt a) Find the function P(t) that satisfies the equation. b) Suppose that $1500 is invested. What is the balance after 3 years? 12

A endangered species is released into a park. The population of an endangered species  is expected to follow the logistic model p(t)= 810/1+8e-188t .  Where t is measured in mionths.  a.  How many endangered species were released into the park? b.  How many endangered species will there be in 5 months? c.  As time goes by, what appears to be the maximum population in the park?

Find the value of an income stream after 19 years if R(t) = 7000e0.03t is the rate of flow of revenue and the income is deposited at a rate of 10 percent compounded continuously. Round intermediate answers to eight decimal places and final answer to two decimal places.