Question

a psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following function. ​f(t)equals startfraction 85 t over 99 t minus 85 endfraction find the rate of change at which the number of facts remembered is changing after 1 hour and after 10 hours.

Answer 1

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:

$f(t)=\frac{85t}{99t-85}$

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

$f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}$

At t=1

$f^{'}(1)=\frac{-7225}{(85-99)^{2}}$

=-36.86

At t=10 hours

$f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}$

=-0.0088