Spendthrift Freddy initially deposits 2,000 dollars in the bank where it earns 12% interest per year. Let b(t) denote the balance of his account at time t years. Spendthrift Freddy's extravagant ways lead to him withdrawing from his account at a rate of  0.004(b(t))^2 dollars per year.

1. write db/dt

2. Use the Taylor polynomial of degree 1of b(t) to estimate b(0.1).

3. Solve the differential equation, subject to the given initial conditions. The solution b(t) can be given implicitly in the formA*log⁡(B*(b/b−C))=t,where log is the natural logarithm. Write below the exact values for A,B,C

4.find lim(b(t) goes to infinity) = ?

Answer rating: 100% (QA)

SOLUTION 1 We can start by using the chain rule to find the derivative of bt dbdt ddt 2000112t 0004bt2 2000 ln112 112t 0008 bt dbdt Simplifying we get ... View the full answer