Answer:
At t=1, Rate of Change=-36.86
At t=10 hours, Rate of Change =-0.0088
Step-by-step explanation:
The function which describes the number of facts of a certain type which are remembered after t hours is given as:
[TeX]f(t)=\frac{85t}{99t-85}[/TeX]
To determine the Rate of Change at the given time, we first look for the derivative of f(t).
Applying quotient rule:
[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]
At t=1
[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]
=-36.86
At t=10 hours
[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]
=-0.0088
