Mr. brown has taken out a loan of value $1,000 with a 5% apr. he has been paying off the loan at a constant rate of r = $150/year. set up a linear ode for the balance of the loan p(t) as a function of time t in years. [if you're having trouble getting started, see example 2 from

= 0.05P - 150

Step-by-step explanation:

Let P(t) be the balance of the loan at time t years,

Let P(t) will satisfy

where r = annual interest rate

          R = per year payment rate

          R = $150/year

          r = = 0.05  

Now we have the following picture,

Interest            Balance          Payment

5%           ⇒          P(t)       ⇒     $150/year

(0.05)

Therefore, a linear ODE satisfied by P(t) is given by

= 0.05P - 150

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step-by-step explanation: