mathematical model into matlab

how can i write the following mathematical model in MATLAB and get answer of (q) for any value of (t) that i want to put in

q(t)= (6.25* 10^9)/(t+500)^3

Answer 1

[KSSV]

Method 1 Anonymous Function

q = @(t) (6.25* 10^9)/(t+500)^3 ;
q(1)

Method 2

t = 1 ; 
q =  (6.25* 10^9)/(t+500)^3 ;

If you have an array of t :

t = 0:0.01:10 ;
q = (6.25* 10^9)./(t+500).^3 ;
plot(t,q)

[Walter Roberson]

Note: the above are not vectorized

[prinesh patel]

if i want to derrive an equation. how should i do.

[prinesh patel]

that equation has derrivative and log

[KSSV]

Read about diff. If you want it symbolic read about syms.

Answer 2

[Walter Roberson]

q =  @(t) (6.25* 10^9)./(t+500).^3 

This will work for vectors or arrays of t.

[prinesh patel]

how should i derrive an equation. it has differentaion and log

[Walter Roberson]

I recommend using the Symbolic Toolbox

[prinesh patel]

i have mailed you what i actually want to get

[Walter Roberson]

Indeed you did email me, but I always assume that email is confidential unless the sender says otherwise. It would not be proper for me to respond in public to confidential information.

[prinesh patel]

(dq/dt)_in=0 kg/min

(dq/dt)_out=15c kg/min

c= q/(2500+5t)

dq/dt= (dq/dt)_in - (dq/dt)_out

dq/dt=0-( q/(2500+5t))15

dq/dt= (-3dt)/(t+500)

Taking log on both sides,

ln⁡q= -3 ln⁡(t+500) +k_1 (where k1 is integration constant)

ln⁡q= ln⁡(t+500) ^(-3)+k_1

q= e^(k_1 )/(t+500)^3

We have q(0) = 50

50= e^(k_1 )/(0+500)^3

e^(k_1 )=6.25* 10^9

q(t)= (6.25* 10^9)/(t+500)^3

how can i make this model in matlab