Question

A company is offering a bank account. The value, in dollars, of the account, is represented by the function A(t)=50,000(1.02)^t, where t represents the number of years since the account was first opened. Determine the average rate of change of the account value from t = 0 to t = 5. Express your answer in the nearest cent. PLS HELP!!!

Answer 1

The average rate of change of the account value from t = 0 to t = 5 is the change in the account value divided by the change in time, or (A(5) - A(0))/(5 - 0).

We can substitute the given function into the equation:

A(t) = 50,000(1.02)^t

So,

A(5) = 50,000(1.02)^5

and

A(0) = 50,000(1.02)^0

Now we can substitute these values in the equation of average rate of change:

(A(5) - A(0))/(5 - 0) = (50000(1.02)^5 - 50000(1.02)^0) / (5-0)

This simplifies to

(50000(1.02)^5 - 50000) / 5

Which is approximately equal to 67,622.05

So the average rate of change of the account value from t = 0 to t = 5 is approximately 67,622.05.