A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by b(x)=625(1.015)x.
The balance in the account increases at what rate per year? Answer by percent,
The rate at which the balance in the account increases per year can be found by finding the derivative of the function b(x)=625(1.015)^x with respect to x.
Taking the derivative, we have:
b'(x) = 625(1.015)^x * ln(1.015)
To find the rate as a percent, we multiply b'(x) by 100%:
b'(x) = 625(1.015)^x * ln(1.015) * 100%
Therefore, the balance in the account increases at a rate of approximately 1.54% per year.