A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3400 per year. The savings account earns 4% interest compounded continuously. (a) Set up a differential equation that is satisfied by f(t), the amount of money in the account at time t. (b) Solve the differential equation in part (a), assuming that f(0) = 0, and determine how much money will be in the account at the end of 16 years. (a) y' = 100* 5y+3400 (Type an expression using y as the variable.) (b) f(t) = 85000

A fish hatchery has 500 fish at time ? = 0. Each year 40 fish are harvested (evenly, throughoutthe year). The population’s instantaneous growth rate is 10% per year. Thus after 1 year, if nofish were harvested, there would be slightly more than 550 fish. a) Create the modeling differential equation for the amount of the number of fish in the hatchery, y, at time t.b) Solve the differential equation.c) Is there a steady-state level of the number of fish in the hatchery?

A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?

Write a differential equation to model this physical situation. Snow is falling at a constant rate of 3/5 in per hour. It is being removed at a constant rate of 45% of the amount of snow on the ground per hour. If we use h(t) as the height of the snow at time t, and the removal of snow began at a height of 4 in --such that h(0)=4 --what would be the equation for the rate of change of the height as a function of time?