0 Question 5 v B on pt \"0 2 Q 99 '3 Details Let yrt) represent your bank account balance, in dollars, after t years. Suppose you start with $30000 in the account. Each year the account earns 55% interest, and you withdraw $5000. Write the differential equation modeling this situation. _ ll 0 Question ? v E 0H pt '0 2 8 99 (D Detai Let yrt) represent your bank account balance, in dollars, after t years. Suppose you start with $40000 in the account. Each year the account earns 85% interest, and you deposit S4000 into the account. This can be modeled with the differential equation: d1; _ = 0.08 4000 (it y + y(0) = 40000 Solve this differential equation for yft} ym =| . Question 8 V E UH pt '0 2 3 99 (3' Details A manufacturer estimates that she can sell a maximum of 70 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 newr market. and after 3 months her total sales are 11 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 year. Total sales at end of the first year: thousand phones Give your answer to at Least I decimal place 0 Question 9 v B on pt '0 2 :5 99 (3 Details Biologists stocked a Lake with 50'] fish and estimated the carrying capacity {the maximal population for the fish of that species in that lake} to be 4100. The number of fish doubLed in the first year. {a} Assuming that the size of the fish population satisfies the logistic equation dP P a=kp(1'f)v determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k=i _ ,|= em = i [b] How long will it take for the population to increase to 2050 (haLf of the carrying capacity]? . It will takel years. . Question 10 ' E UH pt '0 2 3 99 (3' Details 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 I50 thousand cell phones. After 29 thousand cell phones have been sold. sales are increasing by 1" thousand phones per month. Find the differential equation describing the cell phone sales. where yr't} is the number of cell phones [in thousands] sold after t months. Enter at least 3 decimal places for the constants