Exponential equation (simple?)

[1875]

exponential equation (simple??)

x = Ae ^ kt

initally (at t = 0) x = 0.2 and when t = 2 then x = 1.5

a) Find A and k

b) Find x when t = 1.5

c) How long will it take x to decay to x = 0.01

Really struggling, any help would be greatly appreciated.

 

[Rebooter]

x = Ae ^ kt

initally (at t = 0) x = 0.2 and when t = 2 then x = 1.5

a) Find A and k

b) Find x when t = 1.5

c) How long will it take x to decay to x = 0.01

Really struggling, any help would be greatly appreciated.

a) Plug in t=0 and x = 0.2 into the equation.
You get:
0.2 = A*e^0 or A=0.2
(this is like any exponential growth or decay function, at A = the initial value)
plug t = 2 into the equation and you get 0.2e^0.2k=1.5
ln|1.5/0.2|= 0.2k solve for k

b) plug t=1.5 in the equation above x(t) = 0.2e^kt (with whatever you solved for k)

c) same as b but put x = 0.01 in for x and solve for t

 

[fluidistic]

x = Ae ^ kt

initally (at t = 0) x = 0.2 and when t = 2 then x = 1.5

a) Find A and k

b) Find x when t = 1.5

c) How long will it take x to decay to x = 0.01

Really struggling, any help would be greatly appreciated.

Hi and welcome to PF.
Let's try a). When t=0 and x=0.2, can you write up the equation "x = Ae ^ kt"?
This should give you A.

 

[1875]

Thank you, I completely understand it now, just would'nt click at first. I wonder while your online if you could help with;


at time t = 0 and position s = 0 a plane starts its descent into an airfield. From this point, the distance s in km as a function of time t in hours is given by;
s = 300 + 400t - 200t^3

determine
a) the inital velocity (km/hrs)
b) the acceleration after 1/2 hr
c) the time to when the velocity is zero and the distance traveled in that time

deadline tomorrow, pressure on

 

[1875]

Am I right in thinking
a) 300 km/hr
b) 475 km/hr2

 

[Rebooter]

Thank you, I completely understand it now, just would'nt click at first. I wonder while your online if you could help with;


at time t = 0 and position s = 0 a plane starts its descent into an airfield. From this point, the distance s in km as a function of time t in hours is given by;
s = 300 + 400t - 200t^3

determine
a) the inital velocity (km/hrs)
b) the acceleration after 1/2 hr
c) the time to when the velocity is zero and the distance traveled in that time

deadline tomorrow, pressure on

First derivative is velocity so take that and plug in t=0
2nd derivative is acceleration, so take that and plug in t=0.5

 

[1875]

First derivative is velocity so take that and plug in t=0
2nd derivative is acceleration, so take that and plug in t=0.5

I think I am OK on those parts its more the last question that I am having difficulty with;

the time to when the velocity is zero and the distance traveled in that time?

 

[Rebooter]

I think I am OK on those parts its more the last question that I am having difficulty with;

the time to when the velocity is zero and the distance traveled in that time?

Set the first derivative ds/dt = 0 = 400-600t^2 solve for t

Plug t into the first equation and solve for s

 

[1875]

Set the first derivative ds/dt = 0 = 400-600t^2 solve for t

Plug t into the first equation and solve for s

for t I got

t = -400/600^2

Thanks again for your help, one last thing, I am just wondering how you came to this equation of 0 = 400 - 600t^2

 

[Rebooter]

for t I got

t = -400/600^2

Thanks again for your help, one last thing, I am just wondering how you came to this equation of 0 = 400 - 600t^2

basic differentiation rules?

 

[1875]

basic differentiation rules?

I must apologise I am unaware of these rules and still struggling greatly on the last question.

 

[HallsofIvy]

If you are not taking a Calculus course, why are you even attempting a problem involving finding the velocity from a position function? That requires Calculus.