Calculating Minimum of PT = 16.8e0.0697t + 204e-0.356t

[Procrastinate]

Calculate the minimum of P_T = 16.8e^0.0697t + 204e^-0.356t

P_T' = 0.0697 x 16.8e^0.0697t + -.356 x 204e^-0.356t

Stationary points occur when P_T'=0. Therefore:

0=0.0697 x 16.8e^0.0697t + -.356 x 204e^-0.356t

My final answer was that t = 4.29. However, the Graphics Calculator begs to differ and says that it is 5.695.

Attached is my working; where have I gone wrong?

 

[cronxeh]

Well I get t=9.6957

http://www.wolframalpha.com/input/?i=plot+16.8*exp(0.0697*t)+204*exp(-0.356*t),t=5..12"

 

[Procrastinate]

Well I get t=9.6957

http://www.wolframalpha.com/input/?i=plot+16.8*exp(0.0697*t)+204*exp(-0.356*t),t=5..12"

Was that using the natural logarithm or an exponent?

 

[cronxeh]

Was that using the natural logarithm or an exponent?

Up to this point you were doing well, then you decided to start dividing and made an error. Try by multiplying it out first then dividing:

0.356*204*exp(-0.356*t) = 0.0697*16.8*exp(0.0697*t)

It should be

72.624*exp(-0.356*t) = 1.17096*exp(0.0697*t)
62.020*exp(-0.356*t)=exp(0.0697*t)

62.020=exp(0.0697*t)/exp(-0.356*t)

ln(62.020)=ln(exp(0.4257*t))

4.1275 = 0.4257*t

t=9.6957

 

[hgfalling]

In your work, you seem to have changed 0.30 ... into 0.030... a little below the middle of the page.

 

[Procrastinate]

I did that and now I get 9.695...

 

[Procrastinate]

In your work, you seem to have changed 0.30 ... into 0.030... a little below the middle of the page.

I rectified that afterwards. Perhaps what I graphed into my Graphics Calculator is wrong.

 

[Procrastinate]

It is. Silly me.