Advertisements
Advertisements
प्रश्न
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
Advertisements
उत्तर
Let at any instant t, the principal be P .
Here, it is given that the principal increases at the rate of 5 % per year .
\[\frac{dP}{dt} = \frac{5P}{100}\]
\[ \Rightarrow \frac{dP}{P} = \frac{1}{20}dt\]
Integrating both sides, we get
\[\ln P = \frac{t}{20} + \ln C ...........(1) \]
Initially at t = 0, it is given that P = Rs 1000 .
\[\ln 1000 = \ln C\]
Substituting the value of ln C in (1), we get
\[\ln P = \frac{t}{20} + \ln 1000\]
\[\text{ Putting }t = 10, \text{ we get }\]
\[\ln \frac{P}{1000} = 0 . 5\]
\[ \Rightarrow \frac{P}{1000} = e^{0 . 5} \]
\[ \Rightarrow P = 1000 \times 1 . 648\]
\[ = 1648\]
Therefore, Rs 1000 will be worth Rs 1648 after 10 years .
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Show that y = ex (A cos x + B sin x) is the solution of the differential equation \[\frac{d^2 y}{d x^2} - 2\frac{dy}{dx} + 2y = 0\]
Differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} = 0, y \left( 0 \right) = 2, y'\left( 0 \right) = 1\]
Function y = ex + 1
Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x
xy dy = (y − 1) (x + 1) dx
In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).
x2 dy + y (x + y) dx = 0
(y2 − 2xy) dx = (x2 − 2xy) dy
3x2 dy = (3xy + y2) dx
A population grows at the rate of 5% per year. How long does it take for the population to double?
The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.
The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is
The solution of the differential equation \[\frac{dy}{dx} = \frac{ax + g}{by + f}\] represents a circle when
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
`x^2 dy/dx = x^2 +xy - y^2`
Solve:
(x + y) dy = a2 dx
Solve
`dy/dx + 2/ x y = x^2`
y2 dx + (xy + x2)dy = 0
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______
Solve the differential equation `"dy"/"dx" + 2xy` = y
Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]
Solution of `x("d"y)/("d"x) = y + x tan y/x` is `sin(y/x)` = cx
Solve the differential equation
`y (dy)/(dx) + x` = 0
