Rates of Change (1 Viewer)

[sando]

Some help required... thanks ... we just started this 2day

The number of people in a certain city is given by P = 200,000e^0.2t, where t is time in years. Find the rate at which the population of the city will be growing after 5 years i'm angry cos i did this q at my tutor.. but left the working out there

and one more

A radioactive substance has a mass that decreases over time t according to the formula M = 200e^-0.1t Find:
a) the mass of the substance after 20 years
b) the rate of its decrease after 20 years

Thanx in advance

 

[pLuvia]

P=200000e^0.2t
dP/dt=40000e^0.2t
When t=5
dP/dt=40000e

A radioactive substance has a mass that decreases over time t according to the formula M = 200e^-0.1t Find:
a) the mass of the substance after 20 years
b) the rate of its decrease after 20 years

a)M=200e^-0.1t
When t=20
M=200e^-2

b)dM/dt=-20e^-0.1t
When t=20
dM/dt=-20e^-2

 

[SoulSearcher]

1) P = 200000e^0.2t
dP/dt = 40000e^0.2t
sub in t=5 and theres your rate of change for the first question.

2)a) sub in the value t=20 into M = 200e^-0.1t and work out your answer from there
b) M = 200e^-0.1t
dM/dt = -20e^-0.1t
again, sub in t=20 and you should get your answer.

 

[sando]

thanks guys

 

[sando]

New Question

A ball is rolled up a slope at a distance from the base of the slope, after time(t) seconds, given by x = 15t - 3t² metres

a) How far up the slope will the ball roll before it starts to roll back down ?

b) What will its velocity be when it reaches the base of the slope ?

c) How long will the motion of the ball take alltogether ?

 

[sando]

Thanks Webby...

just one question... the answer for (a) is suppossed to be 18.75

 

[SoulSearcher]

He placed a 2 instead of a 4 in the denominator of the final answer for a)