Solve and submit the solution to the following questions. The population of a town grows at a rate proportional to the population at any time as = kp, 1. dp dt a) Find the general solution to the differential equation. b) Find the particular solution if initial population of 425 increases by 12.50% in 12 years. c) What will be the population in 28 years? 2. 5 Newton's law of cooling states that the rate of change of temperature of a substance is proportional to the difference in temperature of the substance and its surroundings. The differential dT K(T-T₂) equation that represents this is dt T corresponding to T = 80°C when t = 0. 3. dR dᎾ where is the constant of proportionality and is time in years. by Ө 0°C, = R Ω . If ambient temperature is ", solve the equation for R. (b) If" The variation of resistance, = αR , where is the temperature coefficient of resistance of aluminium. If " wwwwwwww To , of an aluminium conductor with temperature = 20°C ; find expression for = k(a - x). 0°C a = 38 x 10-4/°C determine the resistance of an is given R = Ro when 2 aluminium conductor at 50°C, correct to 3 significant figures, when its resistance at 0°C is 24.02. wwwwwwwwwwww dx dt 4. The velocity of a chemical reaction is given by where x is the amount transferred a in time t, k is a constant and is the concentration at time t=0 when x=0. Solve the equation and determine x in terms of t.
Solve and submit the solution to the following questions. The population of a town grows at a rate proportional to the population at any time as = kp, 1. dp dt a) Find the general solution to the differential equation. b) Find the particular solution if initial population of 425 increases by 12.50% in 12 years. c) What will be the population in 28 years? 2. 5 Newton's law of cooling states that the rate of change of temperature of a substance is proportional to the difference in temperature of the substance and its surroundings. The differential dT K(T-T₂) equation that represents this is dt T corresponding to T = 80°C when t = 0. 3. dR dᎾ where is the constant of proportionality and is time in years. by Ө 0°C, = R Ω . If ambient temperature is ", solve the equation for R. (b) If" The variation of resistance, = αR , where is the temperature coefficient of resistance of aluminium. If " wwwwwwww To , of an aluminium conductor with temperature = 20°C ; find expression for = k(a - x). 0°C a = 38 x 10-4/°C determine the resistance of an is given R = Ro when 2 aluminium conductor at 50°C, correct to 3 significant figures, when its resistance at 0°C is 24.02. wwwwwwwwwwww dx dt 4. The velocity of a chemical reaction is given by where x is the amount transferred a in time t, k is a constant and is the concentration at time t=0 when x=0. Solve the equation and determine x in terms of t.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Solve and submit the solution to the following questions.
1.
The population of a town grows at a rate proportional to the population at any time as
dp kp,
dt
a) Find the general solution to the differential equation.
b) Find the particular solution if initial population of 425 increases by 12.50% in 12 years.
c) What will be the population in 28 years?
2.
Newton's law of cooling states that the rate of change of temperature of a substance is
proportional to the difference in temperature of the substance and its surroundings. The differential
dT
K(T-To)
equation that represents this is dt
T corresponding to T = 80°C when t = 0.
3.
by
2
dR
d0
Ө =
where is the constant of proportionality and is time in years.
0°C,
=
The variation of resistance,
=aR
R Ω
If ambient temperature is
of an aluminium conductor with temperature
wwwmmmmmmmmmm
α = 38 x 10-4/°C
To =
α
where is the temperature coefficient of resistance of aluminium. If
20°C, find expression for
=
k(a - x).
ᎾᏟ
is given
R = Ro
, solve the equation for R. (b) If
determine the resistance of an
aluminium conductor at 50°C, correct to 3 significant figures, when its resistance at 0°C is 24.02.
when
dx
dt
4.
The velocity of a chemical reaction is given by
where x is the amount transferred
in time t, k is a constant and a is the concentration at time t=0 when x=0. Solve the equation and
determine x in terms of t.
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