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0 section 11, Section 11.5 (2022-23) - Math 129, DETAILS Fall 2022 | WebAssign webassign.net Consider the differential equation dy dx = 0.5(1 + y) Find the equilibrium solutions. Give your answers as equations sepa... 3. 4. 5. [-16 Points] The rate of growth of a tumor is proportional to the size of a tumor. (a) Write a differential equation satisfied by S, the size of the tumor, in mm, as a function of time t. Assume the proportionality constant, k, is positive. dS dt (b) Find the general solution to the differential equation. Use C as your final constant of integration. [-16 Points] DETAILS MY NOTES MY NOTES Money in a bank account grows continuously at an annual rate of r (assume r is the interest rate in decimal form). (a) Write a differential equation satisfied by M, the amount of money in the account at time t, measured in years since 2010. dt (b) Solve the initial value problem if $2800 is put into an account in 2010. Your answer will still have r in it. [-18 Points] DETAILS The rate at which ice forms on a lake is inversely proportional to the thickness of the ice. Suppose the ice is 2 inches thick when t = O and 3 inches thick when t = 5 days.