SOLUTION: Please help with the problem: A satellite has a radioactive isotope for its power supply. The power output in watts after elapsed time t in days since powering up is given by Pt

Question 930450: Please help with the problem:
A satellite has a radioactive isotope for its power supply. The power output in watts after elapsed time t in days since powering up is given by Pt=50e^(-t/2035. The onboard equipment requires 10 watts of power to operate properly. What is the operational life (in years) of the satellite?
Thank You

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The power output in watts after elapsed time t in days since powering up is given by Pt=50e^(-t/2035.
The onboard equipment requires 10 watts of power to operate properly.
What is the operational life (in years) of the satellite?
:
Find t when Pt = 10
50*e^(-t/2035) = 10
divide both sides by 50
e^(-t/2035) = .2
Find the nat log of both sides
ln(e^(-t/2035)) = ln(.2)
the log equiv of exponents
ln(e) = ln(.2)
the ln of e = 1 so we have
= -1.61
multiply both sides by -2035
t = 3275.2 days
which is
3275.2/365 = 8.97 ~ 9 years is the life of the satellite
:
;
You can check this for yourself on your calc
enter: 50*e^(-3275/2035)
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