A satellite which travels around the earth has a power supply that provides power according to the formula:
P = 17200/t + 100
where t is the number of days the satellite is aloft. Find the rate at which power is decreasing after 380 days.
rate in watts/day (enter as a positive number) =
Can you please help me set up the relationship here.
Thanks
To find the rate at which power is decreasing after 380 days, we need to find the derivative of the power function with respect to time. The derivative gives us the rate of change of the power with respect to time.
The given power function is:
P = 17200/t + 100
To find the derivative, we'll use the power rule for differentiation. Since the given function is in the form f(t) = g(t) + h(t), where g(t) = 17200/t and h(t) = 100, we can differentiate each term separately.
The derivative of g(t) = 17200/t can be found using the power rule, which states that the derivative of x^n is n * x^(n-1). Here, n = -1:
g'(t) = -17200/t^2
The derivative of h(t) = 100 is 0, as it is a constant.
Now, we add the derivatives of g(t) and h(t) together to get the derivative of P:
P' = g'(t) + h'(t)
= -17200/t^2 + 0
= -17200/t^2
So, the rate at which power is decreasing after 380 days is given by the derivative of the power function evaluated at t = 380:
P'(380) = -17200/380^2
Calculating this expression gives us the rate of power decrease in watts per day.