Finding the AVG ROC for this problem

[Dustobusto]

Homework Statement

With an initial deposit of $100, the balance in a bank account after t years is f(t)=100(108)^t dollars.
Find the average ROC over the intervals of [0, 0.5] and [0, 1]

Homework Equations

It first describes in the book the manner in which you solve this problem as such:
Δf= f(x₁)-f(x₀), Δx=x₁-x₀
So you calculate the first one, then divide it by the calculated result of the second one

In the book, it gives this example.
--Compute the avg ROC of v with respect to T over the interval [273,300].
Δv/Δt = (20√300 - 20√273)/(300-273) ≈ 15.95/27 ≈ 0.59 m/s per K

The Attempt at a Solution

So, I had already solved a problem for avg ROC using that formula and it was correct. Now, given that the answer to my current problem is in the back of the book, I cannot seem to match it.

My attempt for the ordered pair [0, 0.5] is as follows:

f(t) = 100(108)^0.5-100(108)⁰
Any number to the power of zero = 1, therefore:
100(108)^0.5-100(1)
1,039.230485 - 100 = 939.2304845
This would be the upper half, then divide this by the lower half, or x₁-x₀
which is 0.5 - 0...so

939.2304845 / 0.5 = 1,879.460969. The book gives the answer as 7.8461 for just that ordered pair. Once I figure out where I went wrong, I can figure out the second ordered pair. Appreciate any help.

EDIT: Wow I feel stupid. Ok, well, it is 1.08, not 108. Fixing that, and I get the right answer. Carry on, nothing to see here.

 

[Mark44]

Homework Statement

With an initial deposit of $100, the balance in a bank account after t years is f(t)=100(108)^t dollars.
Find the average ROC over the intervals of [0, 0.5] and [0, 1]

Homework Equations

It first describes in the book the manner in which you solve this problem as such:
Δf= f(x₁)-f(x₀), Δx=x₁-x₀
So you calculate the first one, then divide it by the calculated result of the second one

In the book, it gives this example.
--Compute the avg ROC of v with respect to T over the interval [273,300].
Δv/Δt = (20√300 - 20√273)/(300-273) ≈ 15.95/27 ≈ 0.59 m/s per K

The Attempt at a Solution

So, I had already solved a problem for avg ROC using that formula and it was correct. Now, given that the answer to my current problem is in the back of the book, I cannot seem to match it.

My attempt for the ordered pair [0, 0.5] is as follows:

f(t) = 100(108)^0.5-100(108)⁰
Any number to the power of zero = 1, therefore:
100(108)^0.5-100(1)
1,039.230485 - 100 = 939.2304845
This would be the upper half, then divide this by the lower half, or x₁-x₀
which is 0.5 - 0...so

939.2304845 / 0.5 = 1,879.460969. The book gives the answer as 7.8461 for just that ordered pair. Once I figure out where I went wrong, I can figure out the second ordered pair. Appreciate any help.

EDIT: Wow I feel stupid. Ok, well, it is 1.08, not 108. Fixing that, and I get the right answer. Carry on, nothing to see here.

ROC = rate of change?