With an initial deposit of $100, the balance in a bank account after t years is f(t) = 100(1.07)t dollars

Question

With an initial deposit of $100, the balance in a bank account after t years is

f(t) = 100(1.07)^t dollars

Estimate the instantaneous rate of change at t = 0.5 years by computing the average rate of change on small intervals both to the left and to the right of t = 0.5.

1. Intervals to the left of t = 0.5. Round answers to three decimal places.

Interval	[0,0.5]	[0.4,0.5]	[0.49,0.5]
Average Rate of Change

1. Intervals to the right of t = 0.5. Round answers to three decimal places.

Interval	[0.5,1]	[0.5,0.6]	[0.5,0.51]
Average Rate of Change

1. Use the above to estimate the instantaneous rate of change at t = 0.5 (rounded to two decimal places).

Answer 1

So Roz A.,

This really isn't asking you to do calculus (yet!). Average rate of change means, calculate the function value at each of the endpoints of the interval. Subtract the "initial" from the "final" value, and divide by the interval (delta t) size. That's all! Piece of cake!

Maybe that third question is throwing you for a loop? Of the three intervals in part (2), whic calculation comes closest to being the "instantanteous" = tangent line to the function, for an infinitely small interval? The third one, right? And do you see the three successive calculations of (2) as "pointing" you to an particular value?

-- Cheers, --Mr. d.