Answer to Question #349160 in Differential Equations for cookies

Question

Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5 million pesos. After 2 years, the value decreased to 1.2 million pesos. If the amount of the car is directly proportional to the constant rate of decay in amount and such decrease in amount continues at the same rate, then how much is the estimated value of the car after 10 years?

Answer 1

$$\dfrac{dy}{dt}=-ky$$

$$y(t)=y(0)e^{-kt}$$

Given $y(0)=1500000, y(2)=1200000.$

Then

$$1200000=1500000e^{-k(2)}$$

$$e^k=\sqrt{1.25}$$

$$y(t)=1500000(\sqrt{1.25})^{-t}$$

$$y(10)=1500000(\sqrt{1.25})^{-10}$$

$$y(10)=491520$$

491520 pesos.