QUESTION 1:

\fLet y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $40000 in the account. Each year the account earns 4 % interest, and you withdraw $8000. Write the differential equation modeling this situation. dy_ dt_[ ] y(0) = A manufacturer estimates that she can sell a maximum of 105 thousand cell phones in a city. By advertising heavily, her total sales grow at a rate proportional to the distance below this upper limit. If she enters a new market, and after 5 months her total sales are 9 thousand phones, find a formula for the total sales (in thousands) 1' months after entering the market, and use this to estimate the total sales at the end of the first yea r. Total sales at end of the first year: thousand phones Give your answer to at least 1 decimal place A new cell phone is introduced into the market. It is predicted that sales will grow logistically. The manufacturer estimates that they can sell a maximum of 50 thousand cell phones. After 14 thousand cell phones have been sold, sales are increasing by 6 thousand phones per month. Find the differential equation describing the cell phone sales, where y is the number of cell phones (in thousands) sold after t months. dy_%J (it Enter at least 3 decimal places for the constants.