Question

The equation A=2500(0.96)t represents an account balance t years after the account was created. Which statement is correct?​ A The account balance will decrease 0.04% each year. B The account balance will increase 0.04% each year. C The account balance will decrease 4% each year. D The account balance will increase 4% each year.

Answer 1

C

Explanation:

Here, we want to deduce what would happen to the account balance given the above equation.

A = 2500(0.96)^t

This can be re-written as;

A = 2500(1-0.04)^t

or more generally as A = 2500(1-r)^t

where r is our rate

Now 0.04 is our rate of either increase or decrease, then it is expected to be written as a percentage.

This means that 0.04 is same as 4/100 or just 4%

Now, since there is a negative difference between 1 and r in the bracket or let’s say the term in the bracket is less than 1, then what we shall be expecting is a decrease, year in year out

Thus, the account balance is expected to decrease by 4% each year