With an initial deposit of $100, the balance in a bank account after t years is dollars. Find the average rate of change over [0, 0.5] and [0, 1], then estimate the instantaneous rate of change at t = 0.5.
The rate of change of f(t) is the ratio of the change in f(t) divided by the unit change in t.
The account balance f(t) is measured in dollars and t is measured in years.
The average rate of change of y = f(t) over the interval [t0, t1] is given by the following.
Average rate of change =
Find the average rate of change over the interval [0, 0.5]. (Round your answers to two decimal places.)
For the interval [0.0, 0.5], let t0= 0 and t1 = .
Find the average rate of change over the interval [0, 1]. (Round your answers to two decimal places.)
For the interval [0, 1], let t0= 0 and t1 = .
In this case, f(t1) = 100*(FB:*1.16)1 and f(t0) = 100*(FB:*1.16)0
Recall that the instantaneous rate of change at t = t0 is the limit of the average rates of change.
To estimate the instantaneous rate of change of the given problem, we calculate the average rate of change over smaller and smaller intervals to the of t =