# From First Principles - Page 2

Questions

- How to approach and solve this problem?
- Hi ! How do you resolve #y'(t)=ty(t) + 1# and #y(0) =1# without using #erf(x)# please? Thanks!
- Population y grows according to the equation dy/dx=ky, where k is constant and t is measured in years. If the population doubles every 10 years, then what is the value of k?
- The population of a town a town after t weeks is given by p(t)=1200(2^-t). a) what is the initial population of the town? b) how many people are there after 1 week? c) what is the rate of change of people after 1 week?
- DP-6P dt=0 P=5 when t=0 ?
- What is the differential equation?
- Solve the initial value problem #y'=ky^2\lnx#, with #y(1)=-1#?
- #(dP)/dt=kP# has the function #P(t)=P_0e^(kt)# as its solution. Show by differentiating that this function for #P(t)# does in fact satisfy the differential equations?
- How to do question 4?
- Need help with a growth problem ?
- Please help me solve for k. Not sure what to do?
- Differentiate the following polynomial and algebraic expressions? #y = 7x^3 + 9x^2 - 12x + 60#
- Differentiate (ax+b)raised to the power n by abinitio method?
- Differentiate the following polynomial and algebraic expression y = 9x + 33 ?
- What is the answer ?
- Population P grows according to the equation dP/dt =kP. If the population is initially 12000 and doubles every 8 years, what is the equation for P as a function of t?
- Differentiate the function #f(x)= x/(x+1)# from first principle?
- How do I find the derivative of #x^2 + 7x -4# using first principles?
- You deposit $700 in an account that pays 12% annual interest compounded annually. How do you write a recursive function to model the situation?
- What is the Solution of the Differential Equation # (dP)/dt = kP - AP^2#?